# 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 = πr^{2}h

Capacity of the vessel = 15.4 litres

= 15.4 / 1000 m^{3} (Since, 1000 l = 1m^{3})

= 0.0154 m^{3}

Let the radius of the vessel be r

Height of the vessel, h = 1 m

Volume of the vessel = 0.0154 m^{3}

πr^{2}h = 0.0154 m^{3}

r^{2} = 0.0154 / πh

r^{2} = 0.0154 /1 × 7/22

r^{2} = 0.0049 m^{2}

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 m^{2}

0.4708 m^{2} 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 m^{2} of metal sheet would be needed to make the vessel.

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