A hollow hemisphere and a cone have equal bases. If their heights are also equal, then the ratio of their curved surface area will be:
Explanation:
Let the radius of the hemispere and cone be r.
Height of the hemispehere will also be r, hence height of the cone will be r.
Slant height of the cone (l) = r2+r2 = √2 r
Curved surface area of Hemispere = 1/2 × 4πr2 = 2πr2
Curved surface area of Cone = πrl = π × r × √2r = √2 × πr2
∴ Required ratio = 2πr2 : √2 × πr2 = 2 : √2 = √2 : 1
Hence, option (b).
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