Find the volume of a cone which has a base radius of 5 cm and slant height of 13 cm.
A.
\(300\pi\) cm\(^3\)
B.
\(325\pi\) cm\(^3\)
C.
\(\frac{325}{3}\pi\) cm\(^3\)
D.
\(100\pi\) cm\(^3\)
Correct answer is D
Volume of a cone = \(\frac{1}{3}\pi r^2 h\)
r = 5 cm
l = 13 cm
Using Pythagoras theorem
⇒ \(13^2 = 5^2 + h^2\)
⇒ \(169 = 25 + h^2\)
⇒ \(169 - 25 = h^2\)
⇒ \(h^2 = 144\)
⇒ \(h = \sqrt144 = 12 cm\)
∴ Volume of the cone = \(\frac{1}{3} \times\pi\times 5^2 x 12 = 100\pi\) cm\(^3\)