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.
Answers
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:
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 .