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Math Help - How many scoops are in each container?

  1. #1
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    How many scoops are in each container?

    I'm really stuck on this question.

    Ice cream is sold in stores in cyndrical containers. The containers are 21cm high with a radius of 10cm, and each scoop of icecream is a sphere of diameter 4.2cm. How many scoops are in each container?

    I looked at the answers and it said the answer was 170 scoops.
    Help please?
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  2. #2
    MHF Contributor
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    The entire volume of ice cream in the cylinder must equal the entire volume of all the ice cream scoops.

    Shape allows us to use a volume formula.

    The volume of a cylinder is (circle area)(height) = \pi(r^2)h

    The volume of our cylinder is \pi(10)^221

    The scoops are spherical.

    the volume of a sphere is \frac{4}{3}\pi(r^3)

    The volume of one scoop is \frac{4}{3}\pi(\frac{4.2}{2})^3=\frac{4}{3}\pi(2.1  )^3

    Dividing the cylinder volume by the sphere volume gives the number of scoops, since all those scoops of ice cream makes up the full amount of ice cream in the container.
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