What is the diameter of a hemisphere with a volume of 2233\text{ cm}^3,2233 cm 3 , to the nearest tenth of a centimeter?

Question

What is the diameter of a hemisphere with a volume of 2233\text{ cm}^3,2233 cm 3 , to the nearest tenth of a centimeter?

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Emery 3 days 2021-11-23T20:54:25+00:00 1 Answer 0 views 0

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    2021-11-23T20:55:42+00:00

    Answer:

    The diameter of the hemisphere is 20.4 centimeters.

    Step-by-step explanation:

    The volume of an hemisphere is given by:

    V = \frac{2 \pi r^{3}}{3}

    In this problem, we have that:

    V = 2233

    So

    \frac{2 \pi r^{3}}{3} = 2233

    2\pi r^{3} = 3*2233

    r^{3} = \frac{3*2233}{2\pi}

    r = \sqrt[3]{\frac{3*2233}{2\pi}}

    r = 10.2

    The radius is 10.2 centimeters.

    The diameter is double the radius. So:

    2*10.2 = 20.4

    The diameter of the hemisphere is 20.4 centimeters.

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