A cone and hemisphere have equal curved surface areas and the same radius. What is the ratio of their heights?
Show answer & explanation
Correct answer: A
Explanation
Radius of cone and hemisphere same = r
According to the formula:
Curved surface area of cone = πrℓ
Curved surface area of hemisphere = 2πr²
πrℓ = 2πr²
ℓ = 2r
Height of cone h = √(ℓ² − r²)
= √(4r² − r²)
= √3r
Height of hemisphere = r
Ratio = √3r : r= √3 : 1