Two similar solids have corresponding linear dimensions in the ratio 2:5. If the volume of the smaller solid is 40, what is the volume of…

For similar solids, volumes scale with the cube of the ratio of corresponding lengths. The lengths are in the ratio $2:5$, so the volume ratio is $2^3 : 5^3 = 8:125$. The larger solid's volume is therefore $40 \times \frac{125}{8} = 5 \times 125 = 625$. A common wrong answer is 100, which comes from multiplying by the linear ratio $\frac{5}{2}$ only. Another is 250, from squaring the ratio, $\frac{25}{4} \times 40$, which is the area relationship. Volume involves three dimensions, so the scale factor must be cubed.