The curved surface area of a right circular cone is 156 $\pi$ and the radius of its base is 12 cm. What is the volume of the cone, in cm$^3$?
Answer & explanation
Correct answer: option 2
We know that,
Curved surface area of cone = πrl
Vomume of cone = \(\frac{1}{3}\)πr2h
L2 = r2 + h2
Radius of cone = r = 12 cm
Curved surface area of cone = πrl = 156π
= 12 × l = 156
l = 13
So, put the value of l and r in = l2 = r2 + h2
= 132 = 122 + h2
= h2 = 169 – 144 = 25
= h2 = 25
= h = 5 cm
Volume of cone =\(\frac{1}{3}\) × π × 12 × 12 × 5 = 240π