Question

In each example given below, radius of base of a cylinder and its height are given. Then find the curved surface area and total surface area.
(1) r = 7 cm, h = 10 cm
(2) r = 1.4 cm, h = 2.1 cm
(3) r = 2.5 cm, h = 7 cm
(4) r = 70 cm, h = 1.4 cm
(5) r = 4.2 cm, h = 14 cm

Answer 1

We know that
Curved surface area of a cylinder = $2\mathrm{\pi }rh$
Total surface area = $2\mathrm{\pi }r\left(h+r\right)$
(1) r = 7 cm, h = 10 cm
Curved surface area of a cylinder = $2\mathrm{\pi }rh$ = $2\mathrm{\pi }\times 7\times 10=140\mathrm{\pi }=140\times \frac{22}{7}=440$ sq cm
Total surface area = $2\mathrm{\pi }r\left(h+r\right)$ = $2\times \frac{22}{7}\times 7\left(10+7\right)=748$ sq cm
(2) r = 1.4 cm, h = 2.1 cm
Curved surface area of a cylinder = $2\mathrm{\pi }rh$ = $2\times \frac{22}{7}\times 1.4\times 2.1=18.48$ sq cm
Total surface area = $2\mathrm{\pi }r\left(h+r\right)$ = $2\times \frac{22}{7}\times 1.4\left(2.1+1.4\right)=30.8$ sq cm
(3) r = 2.5 cm, h = 7 cm
Curved surface area of a cylinder = $2\mathrm{\pi }rh$ = $2\times \frac{22}{7}\times 2.5\times 7=110$ sq cm
Total surface area = $2\mathrm{\pi }r\left(h+r\right)$ = $2\times \frac{22}{7}\times 2.5\left(2.5+7\right)=149.28$ sq cm
(4) r = 70 cm, h = 1.4 cm
Curved surface area of a cylinder = $2\mathrm{\pi }rh$ = $2\times \frac{22}{7}\times 70\times 1.4=616$ sq cm
Total surface area = $2\mathrm{\pi }r\left(h+r\right)$ = $2\times \frac{22}{7}\times 70\left(70+1.4\right)=31416$ sq cm
(5) r = 4.2 cm, h = 14 cm
Curved surface area of a cylinder = $2\mathrm{\pi }rh$ = $2\times \frac{22}{7}\times 4.2\times 14=369.6$ sq cm
Total surface area = $2\mathrm{\pi }r\left(h+r\right)$ = $2\times \frac{22}{7}\times 4.2\left(4.2+14\right)=480.48$ sq cm