The volume of a cylinder of height 32 cm and base diameter 36 cm is equal to the volume of a cone of height 24 cm. The curved surface area (in cm2) of the cone is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. .
Radius (r) = 18 cm
Volume of cylinder = πr2h = π × 182 × 32 = 10368π cm3
Let the radius of the cone = R cm
(1/3)π × R2 × 24 = 10368π
⇒ R2 = (10368 × 3)/24 = 1296
⇒ R = 36cm
Slant height (L) = √(362 + 242) = √1872 = 12√13 cm
Curved surface area = πRL = π × 36 × 12√13 = 432√13π cm3