Hemispherical bowl

Geometry Level 3

A hemispherical bowl of radius 9 9 cm is full of water. This is filled in cylindrical bottles of radius 3 3 cm and height 6 6 cm. How many bottles are required to empty the bowl?


The answer is 9.

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2 solutions

Munem Shahriar
Jul 20, 2017

Volume of the hemisphere,

V h = V_h = 2 3 \dfrac{2}{3} π r 3 \pi r^3

V h = V_h = 2 3 \dfrac{2}{3} π 9 3 = 486 π \pi 9^3 = 486\pi

Volume of the cylinder,

V c = π r 2 h V_c = \pi r^2h

V c = π 3 2 × 6 = 54 π V_c = \pi 3^2 \times 6 = 54\pi

Therefore, the number of bottles required \implies 486 π 54 π \dfrac{486\pi}{54\pi} = 9 =\boxed{9}

The volume of a sphere is v = 4 3 π r 3 v=\dfrac{4}{3} \pi r^3 , but a hemisphere is half of a sphere so the volume of a hemisphere is 1 2 ( 4 3 ) ( π r 3 ) = 1 2 ( 4 3 ) ( π ) ( 9 3 ) = 486 π \dfrac{1}{2}\left(\dfrac{4}{3}\right)(\pi r^3)=\dfrac{1}{2}\left(\dfrac{4}{3}\right)(\pi)(9^3)=486 \pi . The volume of a cylinder is π r 2 h = ( 3 2 ) ( 6 ) = 54 π \pi r^2 h=(3^2)(6)=54 \pi . So the number of bottles required is 486 π 54 π = \dfrac{486 \pi}{54 \pi} = 9 \color{#D61F06}\large \boxed{9}

but instead of ''bu t''. Please correct it.

Munem Shahriar - 3 years, 10 months ago

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thanks . . ...

A Former Brilliant Member - 3 years, 10 months ago

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