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1 February, 21:07

A museum has two spherical cannonballs on display. Each cannonball is made of a type of iron that weighs about 463 pounds per cubic foot. a. The diameter of the smaller cannonball is 1 inch less than the diameter of the larger cannonball. Can you determine how much less the smaller cannonball weighs than the larger cannonball

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  1. 1 February, 23:51
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    the smaller cannonball weighs 88.94% less than the bigger cannonball.

    Step-by-step explanation:

    The volume of bigger spherical cannonball is given by

    Vb = (4/3) π (db/2) ³

    Vb = (4/3) πdb³/8

    Vb = (1/6) πdb³

    we know that mass is density into volume

    m = DV

    m = (1/6) πdb³*463

    suppose the mass of bigger cannonball is 1 pound

    1 = (1/6) πdb³*463

    db³ = 6/463*π

    db = ∛6 / (463*π)

    db = 0.160 ft

    the diameter of smaller cannonball is 1 inch less than the diameter of the larger cannonball.

    1 inch = 0.0833 foot

    ds = db - 0.0833

    ds = 0.160 - 0.0833

    ds = 0.077 ft

    The volume of smaller cannonball is

    Vs = (4/3) π (ds/2) ³

    Vs = (4/3) π (0.077/2) ³

    Vs = 0.000239

    The mass of smaller cannonball is

    m = DV

    m = 463*0.000239

    m = 0.1106 lb

    Difference in mass

    difference = (1 - 0.1106/1) * 100

    difference = 88.94%

    Therefore, the smaller cannonball weighs 88.94% less than the bigger cannonball.
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