# Calculus

posted by .

Find the volume of the solid whose base is the region in the xy-plane bounded by the given curves and whose cross-sections perpendicular to the x-axis are (a) squares, (b) semicircles, and (c) equilateral triangles.

for y=x^2, x=0, and y=0
(a) integral (x^2)^2 from 0 to 2=32/5
(b) integral 1/2 pi (1/2x^2)^2 from 0 to 2 = 4pi/5
(c) integral 1/2x^2(1/2)(x^2)(sqrt(3)) from 0 to 2 = 8(sqrt(3))/5

for y=sqrt(x), x=0, x=16, and y=0
(a) integral (sqrt(x))^2 from 0 to 16= 128
(b) integral 1/2pi[(1/2)(sqrtx)]^2 from 0 to 16 = 16 pi
(c) integral 1/2 (sqrtx)(1/2)(sqrt(x))(sqrt(3))=32sqrt(3)

for y=8-x^2, y=x^2
(a) integral (8-2x)^2 from -2 to 2 = 192
(b) integral 1/2 pi [(8-2x^2)/2]^2 from -2 to 2 =256pi/15
(c) integral (8-2x^2)(sqrt3)(4-x^2) from -2 to 2 = 1024(sqrt3)/15

## Similar Questions

1. ### Calculus

Find the volume of the solid whose base is the region in the xy-plane bounded by the given curves and whose cross-sections perpendicular to the x-axis are (a) squares, (b) semicircles, and (c) equilater triangles. y=x^2, x=0, x=2, …
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 cross-sections of the solid perpendicular to the …
3. ### 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 cross-sections of the solid perpendicular to the …
4. ### 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 cross-sections of the solid perpendicular to the …
5. ### calculus

Find the volume of the solid whose base is the region bounded between the curve y=sec x and the x-axis from x=pi/4 to x=pi/3 and whose cross sections taken perpendicular to the x-axis are squares.
6. ### 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 x-axis are semicircles.
7. ### 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 cross-sections perpendicular to the x-axis are squares.
8. ### calculus

The base of a solid in the xy-plane is the first-quadrant region bounded y = x and y = x2. Cross sections of the solid perpendicular to the x-axis are equilateral triangles. What is the volume, in cubic units, of the solid?
9. ### 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 …
10. ### 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 y-axis that are semicircles. b) Find the volume if the …

More Similar Questions