It is required to make a closed cylindrical tank of height 1m and base diameter 140 cm from a metal sheet. How many square metres of the sheet are required for the same?

Academic Mathematics NCERT Class 9

Given: It is required to make a closed cylindrical tank of height 1m and base diameter 140 cm from a metal sheet

To find: How many square metres of the sheet are required for the same.

Solution:

A closed cylinder formed from a metal sheet.

So the area of metal sheet required = Area of cylinder formed from the metal sheet.

Area of cylinder = Curved surface area $+$ Area of circular sheet in top + Area of circular sheet in bottom

Area of cylinder = $2πr h + π r^2+ π r^2$

r = radius of cylinder as well as circle

Diameter = 140 cm

radius = $\frac{Diameter}{2}$ = $\frac{140}{ 2} = 70$

radius = 70 cm

h = height of cylinder = 1 m = 100 cm

π =$ \frac{22}{7}$ (constant)

Substitute all the values in formula ,

Curved surface area = 2πr h

= $2 \times \frac{22}{7} \times 70 \times 100$

= $2 \times 22 \times 10 \times 1000$ [$\frac{70}{ 7}=10$]

= $44 \times 1000 = 44000$

Curved surface area = 44000 sq cm

Area of circular sheet in top = $π r^2$

= $\frac{22}{ 7} \times 70 \times 70$

= $22 \times 10 \times 70$ [ $\frac{70}{ 7} = 10$]

= $22 \times 700 = 15400$

Area of circular sheet in top = 15400 sq cm

Area of circular sheet in bottom = Area of circular sheet in top = 15400 sq cm

Area of cylinder = $44000 + 15400 + 15400$

Area of cylinder = 74800 sq cm

So, the area of sheet required to form a cylinder = 74800 sq cm.

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Updated on: 10-Oct-2022

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