A hemispherical bowl of radius 9 cm is full of water. This is filled in cylindrical bottles of radius 3 cm and height 6 cm. How many bottles are required to empty the bowl?
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The volume of a sphere is v = 3 4 π r 3 , but a hemisphere is half of a sphere so the volume of a hemisphere is 2 1 ( 3 4 ) ( π r 3 ) = 2 1 ( 3 4 ) ( π ) ( 9 3 ) = 4 8 6 π . The volume of a cylinder is π r 2 h = ( 3 2 ) ( 6 ) = 5 4 π . So the number of bottles required is 5 4 π 4 8 6 π = 9
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Volume of the hemisphere,
V h = 3 2 π r 3
V h = 3 2 π 9 3 = 4 8 6 π
Volume of the cylinder,
V c = π r 2 h
V c = π 3 2 × 6 = 5 4 π
Therefore, the number of bottles required ⟹ 5 4 π 4 8 6 π = 9