Find the volume, curved surface area and total surface area of each of the cylinders whose dimensions are:

Solution:

Volume of a cylinder $=\pi r^{2} h$

Lateral surface $=2 \pi r h$

Total surface area $=2 \pi r(h+r)$

(i) Base radius $=7 \mathrm{~cm}$; height $=50 \mathrm{~cm}$

Now, we have the following:

Volume $=\frac{22}{7} \times 7 \times 7 \times 50=7700 \mathrm{~cm}^{3}$

Lateral surface area $=2 \pi r h=2 \times \frac{22}{7} \times 7 \times 50=2200 \mathrm{~cm}^{2}$

Total surface area $=2 \pi r(h+r)=2 \times \frac{22}{7} \times 7(50+7)=2508 \mathrm{~cm}^{2}$

(ii) Base radius $=5.6 \mathrm{~m}$; height $=1.25 \mathrm{~m}$

Now, we have the following:

Volume $=\frac{22}{7} \times 5.6 \times 5.6 \times 1.25=123.2 \mathrm{~m}^{3}$ Lateral surface area $=2 \pi r h=2 \times \frac{22}{7} \times 5.6 \times 1.25=44 \mathrm{~m}^{2}$ Total surface area $=2 \pi r(h+r)=2 \times \frac{22}{7} \times 5.6(1.25+5.6)=241.12 \mathrm{~m}^{2}$

(iii) Base radius $=14 \mathrm{dm}=1.4 \mathrm{~m}$, height $=15 \mathrm{~m}$

Now, we have the following:

Volume $=\frac{22}{7} \times 1.4 \times 1.4 \times 15=92.4 \mathrm{~m}^{3}$

Lateral surface area $=2 \pi r h=2 \times \frac{22}{7} \times 1.4 \times 15=132 \mathrm{~m}^{2}$

Total surface area $=2 \pi r(h+r)=2 \times \frac{22}{7} \times 1.4(15+1.4)=144.32 \mathrm{~cm}^{2}$