# Finding the volume of a solid(3d)

• Mar 22nd 2009, 02:46 PM
hp.phoenix3
Finding the volume of a solid(3d)
Problem: the solid lies between planes and perp. to the x-axis at x=-1 and x=1. the cross-sections perp. to the x-axis between these planes are squares whose base run from the semicircle y=-sqrt1-x^2 tot the semicircle y=sqrt1-x^2.

I tried drawing this in the 3-d form, with the square cross-sections, but what would be the sides? Would it be -sqrt1-x^2 * sqrt1-x^2?
• Mar 22nd 2009, 02:57 PM
skeeter
Quote:

Originally Posted by hp.phoenix3
Problem: the solid lies between planes and perp. to the x-axis at x=-1 and x=1. the cross-sections perp. to the x-axis between these planes are squares whose base run from the semicircle y=-sqrt1-x^2 tot the semicircle y=sqrt1-x^2.

I tried drawing this in the 3-d form, with the square cross-sections, but what would be the sides? Would it be -sqrt1-x^2 * sqrt1-x^2?

$s = \sqrt{1-x^2} - (-\sqrt{1-x^2}) = 2\sqrt{1-x^2}$

$V = \int_{-1}^1 (2\sqrt{1-x^2})^2 \, dx
$
• Mar 22nd 2009, 03:14 PM
hp.phoenix3
Quote:

Originally Posted by skeeter
$s = \sqrt{1-x^2} - (-\sqrt{1-x^2}) = 2\sqrt{1-x^2}$

$V = \int_{-1}^1 (2\sqrt{1-x^2})^2 \, dx
$

Thanks. I get it now.