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21 May, 07:55

A traditional "square" bale of hay is actually in the shape of a rectangular prism. Its dimensions are 2 feet by 2 feet by 4 feet. How many square bales contain the same amount of hay as one large "round" bale?

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  1. 21 May, 11:54
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    First, lets find out the volume of the square bale ...

    The formula for the volume of a rectangular prism is:

    V=l*w*h where l=length w=width h=height

    This is the data that we are told in the problem for the square bale.

    l=2ft

    w=2ft

    h=4ft

    Lets plug the data into the formula to find the volume of a rectangular prism ...

    V=l*w*h

    V=2*2*4

    V (square) = 16 ft³

    Now lets solve for the volume of the round bale, which is a cylinder shape ... The formula for the volume of a cylinder is:

    V=πr²*h where r=radius and h=height of the cylinder

    This is the data that we know from the problem.

    h=4ft

    d=5ft

    in this equation for the volume, we don't need the diameter, but the radius of the circle, so lets solve for the radius

    d=2r where d=diameter and r=radius

    5=2r

    divide both sides by 2

    2.5ft=r

    Now we can solve for the volume of the round bale

    Volume (round) = πr²*h

    Volume (round) = π2.5²*4

    Volume (round) = 6.25π*4

    Volume (round) = 25π

    Volume (round) = 78.5398163397

    round to the nearest tenth

    Volume (round) = 78.5

    To find out how many square bales make up a round bale we use the expression

    v (round) / v (square)

    78.5/16=4.9

    4.9 square bales contain the same amount of hay as one square bale
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