The total surface area of a metallic hemisphere is 1848cm2. The hemisphere is melted to form a solid right circular cone. If the radius of the base of the cone is the same as the radius of the hemisphere, its height is
A
42cm
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B
26cm
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C
28cm
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D
30cm
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Solution
The correct option is C28cm Total surface area of hemisphere =3πr2, where r= radius of hemisphere. ∴3πr2=1848 ⇒3×227×r2=1848⇒r2=1848×73×22=196 r=√196=14cm Volume of hemisphere =23πr3 =23×π×14×14×14cm3=54883πcm3 According to the question, Volume of cone = Volume of hemisphere ⇒13πr2h=54883πcm3⇒r2h=5488 ⇒14×14×h=5488 ∴h=548814×14=28cm.