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 Question from Hannah, a student: If the volume of a cone of height 10 cm is 261.8 cm3, show that this volume is increased by a factor of 8 if the dimensions of the cone are doubled.

Hi Hannah,

I don't like this problem. The numbers given, 10 centimeters and 261.8 cubic centimeters just confuse the issue.

The volume of a cone is given by

$\mbox{volume } = \frac13 \times \pi \; \mbox{(the radius of the base)}^2 \times \mbox{(the height).}$

Suppose you have a cone with the radius of the base $r$ centimeters and the height $h$ centimeters. Write the expression for its volume.

Suppose you have a cone with the radius of the base $2r$ centimeters and the height $2h$ centimeters. Write the expression for its volume. Simplify this expression to see it is 8 times the volume of the first cone.

Penny

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