# geometry

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A wooden pyramid, 12 inches tall, has a square base. A carpenter increases the dimensions of the wooden pyramid by a factor of 5 and makes a larger pyramid with the new dimensions. Describe in complete sentences the ratio of the volumes of the two pyramids.

• geometry -

the actual values of the dimensions make no difference.

If the original base sides are s, the height is h, then the volume v is

v = 1/3 s^2 * h

now, multiply each dimension by 5 and your new volume V is

V = 1/3 (5s)^2 * (5h)
= 1/3 * 25s^2 * 5h
= 125 * 1/3 s^2 * h
= 125v
or, 5^3 * v

scaling the dimensions of a figure by a factor of n means

area is scaled by n^2
volume is scaled by n^3

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