Atraditional “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?

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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