The radius and height of a right circular cone are in the ratio 5 : 12. If its curved surface area is 816.4 cm2, what is the volume of the cone? (Take \(\pi=3.14\))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2,512 cm3
The slant height of a cone is \(l=\sqrt{r^2+h^2}\), its curved surface area is \(\pi rl\) and its volume is \(\displaystyle\frac{1}{3}\pi r^2h\).
Let \(r=5k\) and \(h=12k\); then \(l=\sqrt{25k^2+144k^2}=13k\)
\(3.14\times5k\times13k=816.4\), so \(204.1k^2=816.4\) and \(k^2=4\), \(k=2\)
\(r=10\) cm and \(h=24\) cm
Volume \(\displaystyle=\frac{1}{3}\times3.14\times10^2\times24=3.14\times800=2512\) cm3
