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27 September, 09:12

If the surface area of a cylinder is 288π cm2 with radius of 8 cm, what is the volume of the cylinder?

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  1. 27 September, 09:31
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    The volume of the cylinder is 640π cm³

    Step-by-step explanation:

    The formula of the surface area of a cylinder is SA = 2πrh + 2πr², where r is the radius of its base and h is its height

    The formula of the volume of a cylinder is V = πr²h

    Let us use the formula of the surface area to find the height of the cylinder, then use the formula of the volume to find its volume

    ∵ The surface area of a cylinder is 288π cm²

    ∵ Its radius is 8 cm

    ∵ SA = 2πrh + 2πr²

    - Substitute the SA by 288π and r by 8 in the formula

    ∴ 288π = 2π (8) h + 2π (8) ²

    ∴ 288π = 16πh + 128π

    - Subtract 128π from both sides

    ∴ 160π = 16πh

    - Divide both sides by 16π

    ∴ 10 = h

    ∴ The height of the cylinder is 10 cm

    Now let us find the volume of the cylinder

    ∵ V = πr²h

    - Substitute r by 8 and h by 10

    ∴ V = π (8) ² (10)

    ∴ V = π (64) (10)

    ∴ V = 640π

    The volume of the cylinder is 640π cm³
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