water melon

Geometry Level 3

The water melon shown above is in the shape of a sphere. The diameter is 15 centimeters. It was then cut into two equal pieces. What is the surface area of one piece (in square centimeters)? If your answer can be expressed as a π a\pi , give your answer as a a .


The answer is 168.75.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Note that the surface area of one piece is the surface area of a sphere divided by two plus the area of the portion where it was cut.

S = 1 2 ( 4 π r 2 ) + π r 2 = 2 π ( 7. 5 2 ) + π ( 7. 5 2 ) = 112.5 π + 56.25 π = 168.75 π S=\dfrac{1}{2}(4 \pi r^2)+\pi r^2=2\pi(7.5^2) +\pi(7.5^2)= 112.5\pi +56.25 \pi =168.75 \pi

Finally,

a = 168.75 \color{#D61F06}\large \boxed{a=168.75}

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