The height of a cylinder is 10 and the area of a base is 36 pi square units. What is the volume in cubic units

Question

The height of a cylinder is 10 and the area of a base is 36 pi square units. What
is the volume in cubic units

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Everleigh 3 months 2022-02-15T14:17:35+00:00 1 Answer 0 views 0

Answers ( )

    0
    2022-02-15T14:19:33+00:00

    Answer:

    1130.97336 units^3

    Step-by-step explanation:

    The volume of a cylinder can be found using:

    [tex]v=\pi r^2h[/tex]

    We have the area of the base, but not the radius

    [tex]a=\pi r^2[/tex]

    We know the area is [tex]36\pi[/tex], so we can substitute that in for a

    [tex]36\pi =\pi r^2[/tex]

    We want to find r, so we need to isolate it

    Divide both sides by pi

    36=r^2

    Take the square root of both sides

    6=r

    Now we know the radius, and can substitute it into the volume formula, and we can substitute the height (10) in

    [tex]v=\pi r^2h[/tex]

    [tex]v=\pi 6^210[/tex]

    Solve the exponent

    [tex]v=\pi 36(10)[/tex]

    [tex]v=\pi 360[/tex]

    v=1130.97336

    The volume is 1130.97336 units^3

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