Question #161246

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.


1
Expert's answer
2021-02-24T06:43:28-0500

R1=4 cm, R2=8 cm, l=6 cm

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

Formula volume V=1/3π\pi H (R12+R1R2+R22) for H2=l2-(R2-R1)2 consequently H=3616\sqrt{36-16} =25\sqrt{5} and

V=1/3π\pi 25\sqrt{5} (16+32+64)=224π\pi5\sqrt{5} /3=524.25

Answer: S=24π\pi=75.36 cm2 and V=224π\pi5\sqrt{5} /3=524.25 cm3

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