Question

A small box is enlarged to form a larger similar box. The small box has height 3. The large box has height of 9. If the volume of the smaller box is 60 cubic units, which expression will calculate the volume of the larger box?

Answer 1

• V = 60*27 or 1620 cubic units

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The ratio of the corresponding sides is the scale factor of similar figures.

The scale factor in our case is:

• k = 9/3 = 3

The volume is the product of three dimensions, hence the ratio of volumes of similar shapes is the cube of the scale factor.

Therefore, to find the volume of the larger box we need to multiply the volume of the smaller box by k³ = 3³ = 27.

The expression is:

• V = 60*27

The volume is:

• V = 1620 cubic units