Hemisphere

Geometry Level 2

The volume and surface area of the hemisphere shown above are numerically equal. Find its diameter.


The answer is 9.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

V h e m i s p h e r e = A h e m i s p h e r e V_{hemisphere}=A_{hemisphere}

1 2 ( 4 3 ) ( π ) ( r 3 ) = 1 2 ( 4 π ) ( r 2 ) + π r 2 \dfrac{1}{2}\left(\dfrac{4}{3}\right)(\pi)(r^3)=\dfrac{1}{2}(4\pi)(r^2)+\pi r^2

2 3 r 3 = 3 r 2 \dfrac{2}{3}r^3=3r^2

2 3 r = 3 \dfrac{2}{3}r=3

2 r = d = 9 \boxed{2r=d=9}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Why the extra π r 2 \pi r^2 in the formula for the area of a hemisphere?

Rob Simpson - 3 years, 8 months ago

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That is the area on the top on the hemisphere.

A Former Brilliant Member - 3 years, 8 months ago

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