Question

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

(i) radius of the base = 7 cm and height = 50 cm

(ii) radius of the base = 5.6 m and height = 1.25 m

(iii) radius of the base = 14 dm and height = 15 m

Answer 1

(i)Radius of the base of the cylinder (r)=7 cm.

Height (h)=50 cm.

$\therefore$ (a)Volume $=\pi r^{2}h$

$=\frac{22}{7}\times (7{)}^2\times 50c{m}^2$

$=\frac{22}{7}\times 7\times 50c{m}^3=7700c{m}^3$

(b)Lateral surface area $=2\pi rh$

$=2\times \frac{22}{7}\times 7\times 50=2200c{m}^2$

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

$=2\times \frac{22}{7}\times 7(50+7)c{m}^2$

$=44\times 57=2508c{m}^2$

(ii)Radius of the base of the cylinder (r)

=5.6 m

Height (h)=1.25 m

$\therefore$ (a)Volume $=\pi r^{2}h$

$=\frac{22}{7}\times (5.6{)}^2\times 1.25c{m}^3$

$=\frac{22}{7}\times 5.6\times 5.6\times 1.25m^2=44m^2$

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

$=2\times \frac{22}{7}\times 5.6(1.25+5.6)$

$=44\times 0.8\left(6.85\right)m^2=241.12m^2$

(iii)Radius of the base of a cylinder (r)

=14dm=1.4 m.

Height (h)=15 m

(a)Volume

$=\pi r^{2}h=\frac{22}{7}\times (1.4{)}^2\times 15m^3$

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

(b)Lateral surface area $=2\pi rh$

$=2\times \frac{22}{7}\times 1.4\times 15m^2=132m^2$

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

$=2\times \frac{22}{7}\times 1.4(15+1.4)m^2$

$=8.8\left(16.4\right)m^2=144.32m^2$