Question

The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How much m^2 of metal sheet would be needed to make it?​

Answer 1

Answer:

0.4708 m2

Step-by-step explanation:

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.