QA – Placement Quizzes | Mensuration 3D | Question 8

A hemisphere and a cone have equal bases. If their heights are also equal, then the ratio of their curved surfaces will be:
(A) 1:2
(B) 2:1
(C) 1:2^0.5
(D) 2^0.5:1


Answer: (D)

Explanation: Let r be the radius of the hemisphere and the cone. Given,
Height of Cone = Radius of Hemisphere = r
Slant height of Cone = √(r²+ r²) = √2r
Ratio of their Curved Surfaces = Hemisphere/Cone
= 2 * π * r² / π * r * √2r
= √2:1.

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