Question

the radius of the base of a truncated right circular cylinder is 5 in. and its longest element is 16 in. If the slope of the top plane is 3/4, find the volume of the solid.

Answer 1

$V= \frac{r^2\pi(h_1+h_2)}{2} \\ \\ \frac{3}{4} = \frac{h_1-h_2}{d} \\ \frac{3}{4} = \frac{16-h_2}{5} \\ 4(16-h_2)=5 \times 3 \\64-4h_2=15 \\49=4h_2 \\h_2= \frac{49}{4}=12.25 \\ \\r= \frac{d}{2} \\r=2.5 \\ \\V= \frac{r^2\pi(h_1+h_2)}{2} = \frac{2.5^2\pi(12.25+16)}{2} =88.28 \pi$