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2 August, 09:09

A cylinder with a radius of 12cm and a height of 20cm has the same volume as a cone with a radius of 8cm. What is the height of the cone

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  1. 2 August, 10:25
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    Answer: 135cm

    Step-by-step explanation

    Volume of a cylinder = πr²h

    Volume of a cone. = 1/3πr²h

    The two shapes are both solid shapes.

    Since the have same volume, we can then equate the two together and solve for the height of the cone.

    Now make H the height and R the radius of the cylinder and h the height and r the radius of the cylinder.

    Now equating the two

    πR²H = 1/3πr²h

    Now substitute for the values now

    Multiply through by 3

    3πR²H = πr²h

    But π is common so it could be obliterated from the equation

    3R²H = r²h

    3 x 12² x 20 = 8² x h

    3 x 144 x 20 = 64 x h

    60 x 144 = 64h

    8640. = 64h

    Therefore

    h = 8640/64

    = 135cm
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