Question:
A particular brand of talcum powder is available in two packs, a plastic can with a square base of side 5 cm and of height 14 cm, or one with a circular base of radius 3.5 cm and of height 12 cm. Which of them has greater capacity and by how much?
Solution:
For the cubic pack:
Length of the side, $a=5 \mathrm{~cm}$
Height $=14 \mathrm{~cm}$
Volume $=a^{2} h=5 \times 5 \times 14=350 \mathrm{~cm}^{3}$
For the cylindrical pack:
Base radius $=r=3.5 \mathrm{~cm}$
Height $=12 \mathrm{~cm}$
Volume $=\pi r^{2} \mathrm{~h}=\frac{22}{7} \times 3.5 \times 3.5 \times 12=462 \mathrm{~cm}^{3}$
We can see that the pack with a circular base has a greater capacity than the pack with a square base.
Also, difference in volume $=462-350=112 \mathrm{~cm}^{3}$