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29 March, 16:59

The base of a cylinder has an area of 64π in2. If the height of the cylinder is 10 in., what is the total volume?

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Answers (2)
  1. 29 March, 18:16
    0
    V = 3217.0 m3

    Step-by-step explanation:

    The base area is given and the height is equal to twice the radius.

    Use the formula for the area of a circle to solve for the radius of the cylinder.

    A=πr2

    Substitute 64π for A.

    64π=πr2

    Divide both sides by π.

    64=r2

    Take the positive square root of both sides.

    8=r

    Therefore, the radius is equal to 8 m.

    The height is equal to twice the radius.

    h=2r

    Substitute 8 for r.

    h=2⋅8

    Simplify.

    h=16

    Therefore, the height is equal to 16 m.

    To find the volume of the cylinder, use the formula for the volume of a cylinder, V=πr2h.

    Substitute 8 for r and 16 for h.

    V=π⋅82⋅16

    Simplify.

    V=1024π

    Use a calculator to approximate.

    V≈3217.0 m3

    Therefore, the volume of the cylinder is approximately 3217.0 m3.
  2. 29 March, 20:42
    0
    see explanation

    Step-by-step explanation:

    The volume (V) of a cylinder is

    V = area of base * height

    here area of base = 64π and height = 10, hence

    V = 64π * 10 = 640π in³ ← exact value
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