When two solids are similar the ratio of their volumes is equal to the ratio of their corresponding linear measures cubed.
196 cubic millimeters
Practice makes perfect
We know the lengths of base of two similar pyramids but the volume of just one of them.
When two solids are similar, the ratio of their volumes is equal to the ratio of their corresponding linear measures cubed.
Volume of the smaller solid/Volume of the bigger solid
=
(Height of the smaller solid/Height of the bigger solid)^3
We know that the sides and the volume of the bigger solid are 21 millimeters and 5292 cubic millimeters, respectively. We also know that the sides of the smaller solid are 7 millimeters. If we let V be the volume of the smaller solid, we can substitute these values in the equation and solve for V.
Volume of the smaller solid/Volume of the bigger solid=(Height of the smaller solid/Height of the bigger solid)^3
