Question

Cubical boxes of volume 15625 cm³ each are put in a cubical store of side 2.5 m.

I. How many such boxes can be put in the store?

ii. What are the dimensions of the box?

Answer 1

Volume of cubical boxes = 15625 cm³

Side of cubical store = 2.5 m = 2.5 $\times$ 100 cm = 250 cm

Volume of cubical store = side³ = (250)³ = 15625000 cm³


Thus, number of boxes that store can contain = $\frac{\mathrm{Volume}\mathrm{of}\mathrm{cubical}\mathrm{store}}{\mathrm{Volume}\mathrm{of}1\mathrm{box}}=\frac{15625000}{15625}=1000{\mathrm{cm}}^3$


Dimension of the box = 15625 cm³

$\Rightarrow$ side³ = 15625 cm³

$\Rightarrow$ side = $\sqrt[3]{15625{\mathrm{cm}}^3}=\sqrt[3]{25\times 25\times 25{\mathrm{cm}}^3}=25\mathrm{cm}$

$\Rightarrow$ side of box = 25 cm

Hence, the answer.