MathDB

A solid in Euclidean

3

-space extends from

z = \frac{-h}{2}

z = \frac{+h}{2}

and the area of the section

z = k

is a polynomial in

k

of degree at most

3

. Show that the volume of the solid is

\frac{h(B + 4M + T)}{6},

where

B

is the area of the bottom

(z = \frac{-h}{2})

M

is the area of the middle section

(z = 0),

and

T

is the area of the top

(z = \frac{h}{2})

. Derive the formulae for the volumes of a cone and a sphere.

Problem Statement