What is the volume of the solid with given base and cross sections? The base is the region enclosed by y=x^2 and y=3. The cross sections perpendicular to the yaxis are rectangles of height y^3.
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Calc 2
Find the volume of the solid whose base is the region enclosed by y=x^2 and y=2, and the cross sections perpendicular to the yaxis are squares.

CALCULUS
The base of S is a circular disk with radius 3r. Parallel crosssections perpendicular to the base are isosceles triangles with height 8h and unequal side in the base. a. set up an interval for volume of S b. by interpreting the intergal as an area, find

calculus
#3 A solid has a base in the form of the ellipse: x^2/25 + y^2/16 = 1. Find the volume if every cross section perpendicular to the xaxis is an isosceles triangle whose altitude is 6 inches. #4 Use the same base and cross sections as #3, but change the

Calculus 2
Find the volume of the solid whose base is the semicircle y= sqrt(1− x^2) where −1≤x≤1, and the cross sections perpendicular to the x axis are squares.

Calculus
Find the volume of the solid whose base is the circle x^2+y^2=25 and the cross sections perpendicular to the xaxis are triangles whose height and base are equal. Find the area of the vertical cross section A at the level x=1.

Calculus
The base of a solid is the circle x2 + y2 = 9. Cross sections of the solid perpendicular to the xaxis are equilateral triangles. What is the volume, in cubic units, of the solid? 36 sqrt 3 36 18 sqrt 3 18 The answer isn't 18 sqrt 3 for sure.

Calculus
The base of a solid is the circle x^2 + y^2 = 9. Cross sections of the solid perpendicular to the xaxis are squares. What is the volume, in cubic units, of the solid? A. 18 B. 36 C. 72 D. 144 Please help. Thank you in advance.

calculus
Find the volume V of the described solid S. The base of S is a circular disk with radius 2r. Parallel crosssections perpendicular to the base are squares.

Calculus
Let R be the region enclosed by the graphs y=e^x, y=x^3, and the y axis. A.) find R B.) find the volume of the solid with base on region R and cross section perpendicular to the x axis. The cross sections are triangles with height equal to 3 times the

Calculus (Volume of Solids)
A solid has, as its base, the circular region in the xyplane bounded by the graph of x^2 + y^2 = 4. Find the volume of the solid if every cross section by a plane perpendicular to the xaxis is a quarter circle with one of its radii in the base.

Calculus
Let R be the region in the first quadrant enclosed by the graph of f(x) = sqrt cosx, the graph of g(x) = e^x, and the vertical line pi/2, as shown in the figure above. (a) Write. but do not evaluate, an integral expression that gives the area of R. (b)

calculus review please help!
1) Find the area of the region bounded by the curves y=arcsin (x/4), y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative. 2)Set up, but do not evaluate, the integral which gives

Calculus
The base of a solid is the region enclosed by the graph of x^2 + 4y^2 = 4 and crosssections perpendicular to the xaxis are squares. Find the volume of this solid. a. 8/3 b. 8 pi/3 c. 16/3 d. 32/3 e. 32 pi/3 Thanks in advance! :)

Calculus
The base of a solid in the xyplane is the circle x^2+y^2 = 16. Cross sections of the solid perpendicular to the yaxis are semicircles. What is the volume, in cubic units, of the solid? a. 128π/3 b. 512π/3 c. 32π/3 d. 2π/3

Calculus
Find the volume of the solid whose base is the circle x^2+y^2=64 and the cross sections perpendicular to the xaxis are triangles whose height and base are equal. Find the area of the vertical cross section A at the level x=7.

College Calculus
Find the volume of the solid with given base and cross sections. The base is the unit circle x^2+y^2=1 and the cross sections perpendicular to the xaxis are triangles whose height and base are equal.

Calculus
a solid has as its base the region bounded by the curves y = 2x^2 +2 and y = x^2 +1. Find the volume of the solid if every cross section of a plane perpendicular to the xaxis is a trapezoid with lower base in the xyplane, upper base equal to 1/2 the

Calculus I
The base of a solid is the circle x^2 + y^2 = 9. Cross sections of the solid perpendicular to the xaxis are squares. What is the volume, in cubic units, of the solid?

Calculus
The base of a solid in the xyplane is the firstquadrant region bounded y = x and y = x^2. Cross sections of the solid perpendicular to the xaxis are equilateral triangles. What is the volume, in cubic units, of the solid? So I got 1/30 because (integral

Calculus
The base of a solid is bounded by the curve y=sqrt(x+1) , the xaxis and the line x = 1. The cross sections, taken perpendicular to the xaxis, are squares. Find the volume of the solid a. 1 b. 2 c. 2.333 d. none of the above I got a little confused, but

calculus
Find the volume of a solid whose base is bounded by the parabola x=y^2 and the line x=9, having square crosssections when sliced perpendicular to the xaxis.

Calculus
The base of a solid in the first quadrant of the xy plane is a right triangle bounded by the coordinate axes and the line x + y = 2. Cross sections of the solid perpendicular to the base are squares. What is the volume, in cubic units, of the solid?

Math
Find the volume V of the described solid S. The base of S is a circular disk with radius 4r. Parallel crosssections perpendicular to the base are squares.

calculus
The base of a solid is the circle x2 + y2 = 9. Cross sections of the solid perpendicular to the xaxis are equilateral triangles. What is the volume, in cubic units, of the solid?

calculus
Find the volume V of the described solid S. The base of S is an elliptical region with boundary curve 9x2 + 25y2 = 225. Crosssections perpendicular to the xaxis are isosceles right triangles with hypotenuse in the base.

Calculus
The base of a solid is the circle x^2 + y^2 = 9. Cross sections of the solid perpendicular to the xaxis are equilateral triangles. What is the volume, in cubic units, of the solid? 36√3 36 18√3 18

calculus
The base of a solid is bounded by the curve y= sort (x+2) ,the xaxis and the line x = 1. The cross sections, taken perpendicular to the xaxis, are squares. Find the volume of the solid.

Calculus
Let M be the region under the graph of f(x) = 3/e^x from x=0 to x=5. A. Find the area of M. B. Find the value of c so that the line x=c divides the region M into two pieces with equal area. C. M is the base of a solid whose cross sections are semicircles

Calculus
R is the region in the plane bounded below by the curve y=x^2 and above by the line y=1. (a) Set up and evaluate an integral that gives the area of R. (b) A solid has base R and the crosssections of the solid perpendicular to the yaxis are squares. Find

Calculus
The base of a solid is a circular disk with radius 3. Find the volume of the solid if parallel crosssections is perpendicular to the base are isosceles right triangles with hypotenuse lying along the base.

math
The base of a solid is a region bounded by the curve (x^2/64) + (y^2/16) = 1. Find the volume of the solid if every cross section by a plane perpendicular to the major axis (xaxis) has the shape of an isosceles triangle with height equal to 1/4 the length

math
Can someone please explain this problem to me: I have to use integrals to find volumes with known cross sections but i just don't understand. Thanks! Consider a solid bounded by y=2ln(x) and y=0.9((x1)^3). If cross sections taken perpendicular to the

Calculus
Which of the following is not true? A. In a solid of revolution, the crosssections are circles or washers. B. You can figure the volume of a solid by slicing it into cross sections, figuring the individual volumes, and adding them up. C. You can figure

Calculus
Let f and g be the functions given by f(x)=1+sin(2x) and g(x)=e^(x/2). Let R be the shaded region in the first quadrant enclosed by the graphs of f and g. A. The region R is the base of a solid. For this solid, the cross sections, perpendicular to the

Calculus
The base of a solid is bounded by the curve y=√ x + 1, the xaxis and the line x = 1. The cross sections, taken perpendicular to the xaxis, are squares. Find the volume of the solid.

calculus
1. A solid is constructed so that it has a circular base of radius r centimeters and every plane section perpendicular to a certain diameter of the base is a square, with a side of the square being a chord of the circle. a. Find the volume of the solid. b.

Calculus
R is the region in the plane bounded below by the curve y=x^2 and above by the line y=1. (a) Set up and evaluate an integral that gives the area of R. (b) A solid has base R and the crosssections of the solid perpendicular to the yaxis are squares. Find

CALCULUS 2
Use calculus to find the volume of the following solid S: The base of S is an elliptical region with boundary curve 9x^2+4y^2=36. Crosssections perpendicular to the xaxis are isosceles right triangles with hypotenuse in the base.

calculus
Find the volume of the solid S that satisfies the two following conditions. First, the base of S is the elliptical region with boundary curve 9 x2 + 4 y2 = 36, and second, the crosssections of S perpendicular to the xaxis are isosceles right triangles

calculus
The base of a certain solid is the triangle with vertices at (−6,3), (3,3), and the origin. Crosssections perpendicular to the yaxis are squares. Then the volume of the solid?

AP Calc
The base of a solid is the region in the first quadrant bounded by the ellipse x^2/a^2 + y^2/b^2 = 1. Each crosssection perpendicular to the xaxis is an isosceles right triangle with the hypotenuse as the base. Find the volume of the solid in terms of a

calculus
the base of a solid is a region in the first quadrant bounded by the xaxis, the yaxis, and the line y=1x. if cross sections of the solid perpendicular to the xaxis are semicircles, what is the volume of the solid?

Calc
The base of a solid is a circle of radius a, and its vertical cross sections are equilateral triangles. The volume of the solid is 10 cubic meters. Find the radius of the circle.

Calculus II
Find the volume of the solid whose base is the semicircle y=sqrt(16−x^2) where −4 is less then or equal to x which is less then or equal to 4, and the cross sections perpendicular to the xaxis are squares.

calculus
Find the volume of the solid whose base is the region bounded between the curve y=sec x and the xaxis from x=pi/4 to x=pi/3 and whose cross sections taken perpendicular to the xaxis are squares.

Calculus
The base is an equilateral triangle each side of which has length 10. The cross sections perpendicular to a given altitude of the triangles are squares. How would you go about determining the volume of the solid described? The textbook answer is

Calculus BC
Let the region bounded by x^2 + y^2 = 9 be the base of a solid. Find the volume if cross sections taken perpendicular to the base are isosceles right triangles. (a) 30 (b) 32 (c) 34 (d) 36 (e) 38

Calculus
The base of a solid in the region bounded by the graphs of y = e^x, y = 0, and x = 0, and x = 1. Cross sections of the solid perpendicular to the xaxis are semicircles. What is the volume, in cubic units, of the solid? Answers: 1)(pi/16)e^2

Calculus
The base of a solid is bounded by y=2sqrtx, y=2 and x=4. Find the volume of solid if cross sections perpendicular to y=2 are semicircles

Calculus
The base of a certain solid is the triangle with vertices at (14,7),(7,7) and the origin. Crosssections perpendicular to the yaxis are squares. What is the volume of this solid?

Calculus
The base of a solid in the xyplane is the circle x^2 + y^2 = 16. Cross sections of the solid perpendicular to the yaxis are equilateral triangles. What is the volume, in cubic units, of the solid? answer 1: (4√3)/3 answer 2: (64√3)/3 answer 3:

calculus
The base of a solid is a circle of radius = 4 Find the exact volume of this solid if the cross sections perpendicular to a given axis are equilateral right triangles. The equation of the circle is: x^2 + y^2 = 16 I have the area of the triangle (1/2bh) to

calc
The base of a threedimensional figure is bound by the line y = 6  2x on the interval [1, 2]. Vertical cross sections that are perpendicular to the xaxis are rectangles with height equal to 2. Find the volume of the figure. The base of a

mathematics
The base of a certain solid is the triangle with vertices at (−12,6), (6,6), and the origin. Crosssections perpendicular to the yaxis are squares.

Calculus
Find the volume of the solid whose base is the region in the xyplane bounded by the given curves and whose crosssections perpendicular to the xaxis are (a) squares, (b) semicircles, and (c) equilater triangles. y=x^2, x=0, x=2, y=0 I know how to graph

Calculus AP
Let R be the region in the first quadrant bounded by the graph y=3√x the horizontal line y=1, and the yaxis as shown in the figure to the right. Please show all work. 1. Find the area of R 2. Write but do not evaluate, an integral expression that gives

Calculus
This problem set is ridiculously hard. I know how to find the volume of a solid (integrate using the limits of integration), but these questions seem more advanced than usual. Please help and thanks in advance! 1. Find the volume of the solid formed by

calc
What is the volume of the solid with given base and cross sections? The base is the region enclosed by y=x^2 and y=3. The cross sections perpendicular to the yaxis are rectangles of height y^3.

Calculus
Hi, I have a calculus question that I just cannot figure out, it is about volume of cross sections. I would very much appreciate it if someone could figure out the answer and show me all the steps. A solid has as its base the region bounded by the curves y

Calculus
Hi, I have a calculus question that I just cannot figure out, it is about volume of cross sections. I would very much appreciate it if someone could figure out the answer and show me all the steps. A solid has as its base the region bounded by the curves y

Calculus
The base of a solid in the first quadrant of the xy plane is a right triangle bounded by the coordinate axes and the line x+y =4. Cross sections of the solid perpendicular to the base are squares. What is the volume, in cubic units , of the solid? A) 8 B)

math
Let M be the region under the graph f(x) = 3/(e^x) from x = 0 to x = 5. M is the base of a solid whose cross sections are semicircles whose diameter lies in the xy plane. The cross sections are perpendicular to the xaxis. Find the volume of this solid. 

math
Can someone please explain this problem to me: I have to use integrals to find volumes with known cross sections but i just don't understand. Thanks! Consider a solid bounded by y=2ln(x) and y=0.9((x1)^3). If cross sections taken perpendicular to the

Calculus
Find the volume of the solid whose base is the region bounded by y=x^2 and the line y=0 and whose cross sections perpendicular to the base and parallel to the xaxis are semicircles.

AP Calc B/C
The base of a solid is the region enclosed by y=x^3 and the xaxis on the interval [0,4]. Cross sections perpendicular to the xaxis are semicircles with diameter in the plain of the base. Write an integral that represents the volume of the solid. I drew a

Calculus
The base of a solid is the circle x^2+y^2=9. Cross sections of the solid perpendicular to the xaxis are semicircles. What is the volume, in cubics units, of the solid? a) 9 π/4 b) 18π c) 9π d) 72π

calculus
The base of a certain solid is the triangle with vertices at (10,5), (5,5), and the origin. Crosssections perpendicular to the yaxis are squares. What is the volume of the solid?

calculus
volume of solid whose base is a circle with radius a, and cross sections of the solid cut perpendicular to the xaxis are squares

calculus
the region bounded by the quarter circle (x^2) + (y^2) =1. Find the volume of the following solid. The solid whose base is the region and whose crosssections perpendicular to the xaxis are squares.

Calculus (Volumes)
A solid has as its base the region bounded by the curves y = 2x^2 +2 and y = x^2 +1. Find the volume of the solid if every cross section of a plane perpendicular to the xaxis is a trapezoid with lower base in the xyplane, upper base equal to 1/2 the

Calculus
compute the volume of the following solid the base is a triangular region with vertices (0,0), (2,0), (1,1). Crosssections perpendicular to the yaxis are equilateral triangles.

Calculus
A solid has as its base a circular region in the xy plane bounded by the graph of x^2 + y^2 = 4. Find the volume of a solid if every cross section by a plane perpendicular to the xaxis is an isosceles triangle with base on the xy plane and altitude equal

calculus (please help)
find the volume of the solid whose bounded by the circle x^2+y^2=4 and whose cross sections perpendicular to the yaxis are isosceles right triangles with one leg in the base. Please give explanation and steps

calc
the base of s is a elliptical region with boudary cuvrve 16x^2 +16y^2 =4. cross sections perpandicular to the x axis are isosceles right triangles with hypotenuse in the base. find the volume of s

Calc
The base of a solid is the unit circle x^2 + y^2 = 4, and its crosssections perpendicular to the xaxis are rectangles of height 10. Find its volume. Here's my work: A for rectangle=lw A=10*sq(4x) V= the integral from 4 to 4 of sq(4x^2)*10dx But that

Calculus check
Can someone check my answers: 1) Use geometry to evaluate 6 int 2 (x) dx where f(x) = { x, 2

calculus
Find the volume V of the described solid S. The base of S is the region enclosed by the parabola y = 3 − 2x2 and the x−axis. Crosssections perpendicular to the y−axis are squares.

calculus
The base of a solid consists of the region bounded by the parabola y=rootx, the line x=1 and the xaxis. Each cross section perpendicular to the base and the xaxis is a square. Find the volume of the solid.

Calculus
I would like to make sure my answer is correct: Question: the base of a solid is the triangular region with the vertices (0,0), (2,0), and (0,4). Cross sections perpendicular to the xaxis are semicircles. Find the volume of this solid. My Work: ∫[0,2]

Calculus
R is the region in the plane bounded below by the curve y=x^2 and above by the line y=1. (a) Set up and evaluate an integral that gives the area of R. (b) A solid has base R and the crosssections of the solid perpendicular to the yaxis are squares. Find

math
Can someone please explain this problem to me: I have to use integrals to find volumes with known cross sections but i just don't understand. I have to do a lot of examples for homework like this so can someone show me so I can do my other problems?

calc
he base of a solid in the xyplane is the circle x^2 + y^2 = 16. Cross sections of the solid perpendicular to the yaxis are semicircles. What is the volume, in cubic units, of the solid?

Calculus
The base of a solid is the circle x2 + y2 = 9. Cross sections of the solid perpendicular to the xaxis are semicircles. What is the volume, in cubic units, of the solid?

calc
The base of a solid in the region bounded by the graphs of y = e^x y = 0, and x = 0, and x = 1. Cross sections of the solid perpendicular to the xaxis are semicircles. What is the volume, in cubic units, of the solid?

calculus
The base of a solid in the xyplane is the firstquadrant region bounded y = x and y = x2. Cross sections of the solid perpendicular to the xaxis are equilateral triangles. What is the volume, in cubic units, of the solid?

Calculus
The base of a solid is the region bounded by the lines y = 5x, y = 10, and x = 0. Answer the following. a) Find the volume if the solid has cross sections perpendicular to the yaxis that are semicircles. b) Find the volume if the solid has cross sections

calculus
The base of a certain solid is the triangle with vertices at (10,5), (5,5), and the origin. Crosssections perpendicular to the yaxis are squares. What is the volume of the solid?

Calculus
The base of a solid in the xyplane is the firstquadrant region bounded y = x and y = x^2. Cross sections of the solid perpendicular to the xaxis are equilateral triangles. What is the volume, in cubic units, of the solid? May I have all the explanation

Calculus
The base of a solid is a region located in quadrant 1 that is bounded by the axes, the graph of y = x^2  1, and the line x = 2. If crosssections perpendicular to the xaxis are squares, what would be the volume of this solid?

calculus
The base of a solid V is the region bounded by y=(x^2/64) and y=sq(x/8) Find the volume if V has square cross sections

calculus
The base of a certain solid is the triangle with vertices at (14,7), (7,7), and the origin. Crosssections perpendicular to the yaxis are squares. What is the volume?

Calculus (area of base and volume of solid)
Can you check my work and see if I did the problem correctly? Thanks! A solid with a base formed by intersecting sine and cosine curves and built up with semicircular crosssections perpendicular to the xaxis. Find the area of the base and the volume of

calculus
find the volume of the solid whose base is bounded by the graphs of y= x+1 and y= (x^2)+1, with the indicated cross sections taken perpendicular to the xaxis. a) squares b) rectangles of height 1 the answers are supposed to be a. 81/10 b. 9/2 help with at

math
ind the volume of the solid whose base is bounded by the graphs of y= x+1 and y= (x^2)+1, with the indicated cross sections taken perpendicular to the xaxis. a) squares b) rectangles of height 1 the answers are supposed to be a. 81/10 b. 9/2 help with at

math
find the volume of the solid whose base is bounded by y=e^(x), y=3cos(x), and x=0 and whose cross sections cut by planes perpendicular to the xaxis are squares the answer is 3.992 units cubed but can someone explain to me how to get this answer using

Calculus
The base of a certain solid is the triangle with vertices at (10,5), (5,5), and the origin. Crosssections perpendicular to the yaxis are squares.

calculus
The base of a certain solid is the triangle with vertices at (10,5), (5,5), and the origin. Crosssections perpendicular to the yaxis are squares.

calculus
Find the volume of the solid whose base of a solid is the region bounded bythegraphsofy=3x,y=6,andx=0. Thecross␣sections perpendicular to the x ␣ axis are rectangles of perimeter 20.

calculus
Find the volume of the solid whose base of a solid is the region bounded bythegraphsofy=3x,y=6,andx=0. Thecross␣sections perpendicular to the x ␣ axis are rectangles of perimeter 20.

calculus
The base of a solid is a circle of radius = 4 Find the exact volume of this solid if the cross sections perpendicular to a given axis are equilateral right triangles. I have the area of the triangle (1/2bh) to be equal to 2sqrt(12) (1/2 * 4 * sqrt12) I