Answer to Question #161246 in Geometry for an

Question

Find the volume and the lateral area of a frustum of a right circular cone whose radii are 4 cm and 8 cm, and the slant height is 6 cm.

Answer 1

R₁=4 cm, R₂=8 cm, l=6 cm

Formula lateral area S=1/3$\pi$(R₁+R₂)l consequently S=1/3$\pi$(4+8)6=24$\pi$=75.36

Formula volume V=1/3$\pi$ H (R₁²+R₁R₂+R₂²) for H²=l²-(R₂-R₁)² consequently H=$\sqrt{36-16}$ =2$\sqrt{5}$ and

V=1/3$\pi$ 2$\sqrt{5}$ (16+32+64)=224$\pi$$\sqrt{5}$ /3=524.25

Answer: S=24$\pi$=75.36 cm² and V=224$\pi$$\sqrt{5}$ /3=524.25 cm³