Chapter 6 - Applications of the Integral - 6.2 Setting Up Integrals: Volume, Density, Average Value - Exercises - Page 296: 3

a) $r$ = $\frac{R(h-y)}{h}$ b) $V$ = $\frac{\pi{R}^{2}h}{3}$

a) R = radius of cone h = height of cone r = radius and height y $\frac{h}{h-y}$ = $\frac{R}{r}$ $r$ = $\frac{R(h-y)}{h}$ b) $V$ = $\int_0^h(\frac{R(h-y)}{h})^{2}dy$ $V$ = $\frac{-h\pi}{3R}[\frac{R(h-y)}{h}]^{3}|_0^h$ $V$ = $\frac{\pi{R}^{2}h}{3}$