Question

6. capacity of the vessel. 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? ​

Answer 1

Answer:

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

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

= 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 $m^{3}$

π$r^{2}$h = 0.0154 $m^{3}$

$r^{2}$ = 0.0154 / πh

$r^{2}$ = 0.0154 /1 × 7/22

$r^{2}$ = 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 $m^{2}$