(b) A cylinder of cross-sectional area 0.65m2 and height 0.32m has a mass of 2. Ikg. If there is a cavity inside, find the volume

Question

(b) A cylinder of cross-sectional area 0.65m2 and
height 0.32m has a mass of 2. Ikg. If there is a
cavity inside, find the volume of the cavity.
(Density of cylinder = 11.053 kg/m^3)​

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Lệ Thu 4 years 2021-08-11T12:03:54+00:00 1 Answers 35 views 0

Answers ( )

  1. Sigrid
    0
    2021-08-11T12:05:02+00:00
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    Answer:

    The volume of the cavity is 0.013m^3

    Explanation:

    To find the volume of the cavity, the major parameter missing is the diameter of the cavity itself. we can obtain this using the following steps:

    Step one:

    Obtain the volume of the cylinder by dividing the mass of the cylinder by the density.

    Volume of the cylinder = 2.1 / 11.053 =0.19m^{3}

    Step two:

    From the volume of the cylinder, we can get the radius of the cylinder.

    radius = \sqrt{\frac{V}{\pi \times h}} = \sqrt{\frac{0.19}{\pi \times 0.32}} =0.44m

    Step three:

    From the cross-sectional area, we can obtain the radius of the cavity.

    Let the radius of the cavity be = r, while the radius of the cylinder be = R

    CSA of cavity =

    \pi({R^2}-r^2) = CSA\\0.65 = \pi (0.32^2-r^2)\\r= 0.115m

    Step Four:

    calculate the volume of the cavity using volume =\pi r^2 \times h

    Recall that the cavity has the same height as the original cylinder

    volume = \pi \times 0.115^2\times 0.32= 0.013m^3

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