Question

Find the volume in cubic decimetre of each of the cubes whose side is
(i) 1.5 m
(ii) 75 cm
(iii) 2 dm 5 cm

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right) \\ \mathrm{Side}\mathrm{of}\mathrm{the}\mathrm{cube}=1.5\mathrm{m} \\ =1.5\times 10\mathrm{dm}(\because 1\mathrm{m}=10\mathrm{dm}) \\ =15\mathrm{dm} \\ \therefore \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cube}=(\mathrm{side}{)}^3=(15{)}^3=3375{\mathrm{dm}}^3 \\ \left(\mathrm{ii}\right) \\ \mathrm{Side}\mathrm{of}\mathrm{the}\mathrm{cube}=75\mathrm{cm} \\ =75\times \frac{1}{10}\mathrm{dm}(\because 1\mathrm{dm}=10\mathrm{cm}) \\ =7.5\mathrm{dm} \\ \therefore \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cube}=(\mathrm{side}{)}^3=(7.5{)}^3=421.875{\mathrm{dm}}^3 \\ \left(\mathrm{iii}\right) \\ \mathrm{Side}\mathrm{of}\mathrm{the}\mathrm{cube}=2\mathrm{dm}5\mathrm{cm} \\ =2\mathrm{dm}+5\times \frac{1}{10}\mathrm{dm}(\because 1\mathrm{dm}=10\mathrm{cm}) \\ =2\mathrm{dm}+0.5\mathrm{dm} \\ =2.5\mathrm{dm} \\ \therefore \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cube}=(\mathrm{side}{)}^3=(2.5{)}^3=15.625{\mathrm{dm}}^3 \end{gathered}$$