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Question

# The total surface area of a metallic hemisphere is 1848 cm2. 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
42 cm
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B
26 cm
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C
28 cm
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D
30 cm
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Solution

## The correct option is C 28 cmTotal surface area of hemisphere =3πr2, where r= radius of hemisphere.∴3πr2=1848⇒3×227×r2=1848⇒r2=1848×73×22=196r=√196=14 cmVolume of hemisphere =23πr3=23×π×14×14×14 cm3=54883πcm3According to the question,Volume of cone = Volume of hemisphere⇒13πr2h=54883πcm3⇒r2h=5488⇒14×14×h=5488∴h=548814×14=28 cm.

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