Question

The capacity of a closed cylindrical vessel of height 1m is 1540 liters. Find the radius of the cylinder and also the area of the metal sheet needed to make it.

Answer 1

Given:-

• Height of the vessel = 1m
• Capacity of the vessel = 1540liters = 1.54m^3

Solution :-

Volume of cylindrical vessel = πr²h

1.54 = 22/7 × r² × 1

r² = 1.54 × 7/22

r² = 0.49

r = 0.7m

Now,

Metal sheet needed to make the cylindrical vessel will be equal to the T.S.A of the cylindrical vessel.

TSA = 2πr(r+h)

TSA = 2 × 22/7 × 0.7 ( 0.7+1)

TSA = 30.8/7 (0.7+1)

TSA = 52.36/7

TSA = 7.48m²

So, 7.48m² of metal sheet were needed to make it.

Answer 2

Answer:

Given :-

• The capacity of a closed cylindrical vessel of height is 1 m is 1540 litres.

To Find :-

• What is the radius of the cylinder and the area of the metal sheet needed to make it.

Formula Used :-

★ Volume of a cylinder = πr²h ★

✰ Total surface area of a cylinder = 2πr(r + h) ✰

Solution :-

❶ First we have to find the radius of a cylinder,

Given :

• Height of the vessel = 1 m
• Capacity of the vessel = 1540 litres = 1540/1000 = 1.54 m³

According to the question by using the formula we get,

⇒ πr²h = 1.54

⇒ 22/7 × r² × 1 = 1.54

⇒ r² = 1.54 × 7/22

⇒ r² = 10.78/22

⇒ r² = 0.49

⇒ r = √0.49

➠ r = 0.7 m

∴ The radius of the cylinder is 0.7 m .

❷ Now we have to find the area or total surface area of the cylinder,

Given :

• Radius of the vessel = 0.7 m
• Height of the vessel = 1 m

According to the question by using the formula we get,

↦ T.S.A of the cylinder = 2 × 22/7 × 0.7(0.7 + 1)

↦ T.S.A of the cylinder = 2 × 22/7 × 0.7 × 1.7

↦ T.S.A of the cylinder = 2 × 22/7 × 1.19

↦ T.S.A of the cylinder = 6.29 × 1.19

➦ T.S.A of the cylinder = 7.58 m²

∴ The sheet will be required to make the vessel is 7.58 m² .