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The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?

Solution:

Since the cylinder is a closed vessel, a metal sheet would be needed for the curved surface area and area of the two bases, top and bottom, that is TSA of the cylinder.

Hence, area of the metal sheet will be equal to TSA of the cylinder.

TSA of a cylinder of base radius r, and height h = 2πr(r + h)

Volume of a cylinder of base radius r, and height h = πr2h

Capacity of the vessel = 15.4 litres

= 15.4 / 1000 m3 (Since, 1000 l = 1m3)

= 0.0154 m3

Let the radius of the vessel be r

Height of the vessel, h = 1 m

Volume of the vessel = 0.0154 m3

πr2h = 0.0154 m3

r2 = 0.0154 / πh

r2 = 0.0154 /1 × 7/22

r2 = 0.0049 m2

Thus, r = 0.07 m

TSA of the cylinder = 2πr(r + h)

= 2 × 22/7 × 0.07m × (0.07m + 1m)

= 0.44 m × 1.07 m

= 0.4708 m2

0.4708 m2 of metal sheet would be needed to make the vessel.

☛ Check: NCERT Solutions Class 9 Maths Chapter 13

Video Solution:

The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?

NCERT Solutions for Class 9 Maths Chapter 13 Exercise 13.6 Question 6

Summary:

It is given that the capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. We have found that 0.4708 m2 of metal sheet would be needed to make the vessel.

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