The radius and height of a right circular cone are in the ratio 3 : 4. If its curved surface area (in cm2) is 240π, then its volume (in cm3) is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 768π
Given
Ratio of radius and height of the cone = 3 ∶ 4
Curved surface area = 240 π cm2
We know that
CSA of cone = π r l
where l = √(h2 + r2)
According to the question
Let radius and height = 3x and 4x
l = √[(4x)2 + (3x)2]
= 5x
π r l = 240 π
Putting the values of r and l
π × 3x × 5x = 240 π
Upon Solving
x = 4
Radius = 12 cm
Height = 16 cm
Slant height = 20 cm
We know, volume of cone = 1/3 π x r x r x h
Putting the values of r and h
(1/3) × π × 12 x 12 × 16
= 768π