The volume of a right circular cone is 80% of that of a right circular cylinder whose height is 50% more than that of the cone. If the radius of the cone is 36 cm, then find the radius of the cylinder.
Show answer & explanation
Correct answer: B
Explanation
Given:
Radius of the cone = 36 cm
Height of the cylinder = 50% more than the height of the cone
By the formula:
Volume of the cone = (1/3) πr₁r₁h
Volume of the cylinder = πr₂r₂H
Let the height of the cone = h
Height of the cylinder
H = 1.5h
(1/3)π × 36 × 36 × h = 80% × π × r × r × 1.5h
(1/3) × 1296 × h = 0.8 × 1.5 × r² × h
432h = 1.2 r² h
432 = 1.2 r²
r² = 432 / 1.2
r² = 360
r = √360 = 6√10 cm