JAMB Mathematics 2021 Paper

Concept:For similar solids, the ratio of volumes is the cube of the ratio of corresponding lengths.Explanation:Given linear ratio $2:3$, the lengths scale from smaller to larger by the factor $\frac{3}{2}$.Because the blocks are similar cuboids, all three dimensions scale by the same factor.Therefore, the volume scale factor from smaller to larger is:$$\left(\frac{3}{2}\right)^3 = \frac{27}{8}$$Let the smaller block volume be $V$.Since the larger block volume is $351\,\mathrm{cm}^3$,$$\frac{27}{8}V = 351$$$$V = 351 \times \frac{8}{27}$$$$V = 13 \times 8 = 104\,\mathrm{cm}^3$$Answer:$104\,\mathrm{cm}^3$