The base of S is a circular disk with radius 4r. Parallel cross-sections perpendicular to the base are squares.
Find the volume V of this solid.
I'd write out my work on this problem, but I don't know how to use the thing that lets you do that.
The base of S is a circular disk with radius 4r. Parallel cross-sections perpendicular to the base are squares.
Find the volume V of this solid.
I'd write out my work on this problem, but I don't know how to use the thing that lets you do that.
$\displaystyle x^2 + y^2 = (4r)^2
$
side of a square cross-section perpendicular to the x-axis = $\displaystyle 2y$
area of a square cross-section = $\displaystyle 4y^2$
$\displaystyle dV = 4y^2 dx$
$\displaystyle dV = 4(16r^2-x^2) \, dx$
$\displaystyle V = 2\int_0^{4r} 4(16r^2-x^2) \, dx$