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Math Help - Cylindrical tank

  1. #1
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    Cylindrical tank

    A cylindrical tank has a radius of 30cm and a height of 45cm. The tank contains water to a depth of 36cm.

    A metal sphere is dropped into the water and is completely covered. The water level rises by 5cm.

    What is the radius of the metal sphere?
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  2. #2
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    The increase in volume is {\pi} x 30 x 30 x 5 = 14137.19994 cm^3.

    So the volume of the sphere is 14137.19994 cm^3

    Volume Sphere = \frac {4}{3}{\pi}r^3

    So 14137.19994 = \frac {4}{3}{\pi}r^3 - solving for r we get 15cm.
    Last edited by brennan; October 25th 2010 at 02:45 PM.
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  3. #3
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    Quote Originally Posted by Natasha1 View Post
    A cylindrical tank has a radius of 30cm and a height of 45cm. The tank contains water to a depth of 36cm.

    A metal sphere is dropped into the water and is completely covered. The water level rises by 5cm.

    What is the radius of the metal sphere?
    The water level rise has a "cylindrical shape" as the water is inside a cylinder.
    The water rises by the volume of the sphere.

    Volume of a spherical shape =\displaystyle\frac{4}{3}{\pi}r^3

    Volume of a cylindrical shape ={\pi}R^2h

    To easily cancel terms...

    \displaystyle\frac{4}{3}{\pi}r^3={\pi}R^2h={\pi}30  ^2(5)

    \displaystyle\ r^3=\frac{15(2)15(2)5(3)}{4}=\frac{15^2(15)4}{4}=1  5^3
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