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Question

# A building is in the form of a cylinder surmounted by a hemispherical dome. The base diameter of the dome is equal to 13 of the total height of the building. If the base radius of the cylinder is 6 cm, then the volume of the building is

A

1728π cm3

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B
729π cm3
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C
1224π cm3
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D
1024π cm3
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Solution

## The correct option is C 1224π cm3Let r and h be the base radius and height of the cylinder respectively. So, the total height of the dome is (h+r). Diameter of hemispherical dome = 13×Total height of the building ⇒2r=13(h+r) ⇒2×6=13(h+6) (Given: r=6 cm) ⇒36=h+6 ⇒h=30 cm ∴ Volume of building = Volume of cylinder + Volume of hemisphere =πr2h+23πr3 =πr2(h+2r3) =π×62(30+2×63) =36π×34 =1224π cm3 Hence, the correct answer is option (c).

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