Math CentralQuandaries & Queries


Question from Laura, a student:

There is a cylinder which has a diameter of 10cm and height of 10 cm. Work out the volume of the cylinder. Then in a packed box of 20 cylinders (height of box 10cm) work out the volume inside the box that is not filled by the cylinders give your answer in terms of pi.

Hi Laura,

The volume of a cylinder is the area of the base times the height. Your base is a circle of diameter 10 cm so its radius is 5 cm. Thus the area of the base is π r2 = π 52 = 25 π square centimeters. Hence the volume is 25 π × height = 250 π cubic centimeters.

To find the volume of the box find the area of the base (length × width) and then multiply by the height, 10 cm. This will give the volume in cubic centimeters. The second part of the problem asks for the volume of the box minus the total volume of 20 cylinders.

I hope this helps,

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