A closed cylindrical tank is made up of a sheet of metal. The height of the tank is 1.3m and radius is 70cm. How much sq.m of metal was required ?
Answers
Required Answer :
The total amount of metal required to make the metal sheet = 8.8 m²
Given :
• A closed cylindrical tank is made up of a sheet of metal.
• Height of the tank = 1.3 m
• Radius of the tank = 70 cm
To find :
• How much m² of metal is required to make the metal sheet
Concept :
Firstly, we will convert the value of radius of the tank from cm into m. Then by using the formula of total surface area of cylinder we will find its value. And the total surface area of cylinder will be equal to the area of metal required to make the metal sheet.
Formula to calculate the total surface area of cylinder :-
- TSA = 2πr(r + h)
where,
- Take π = 22/7
- r denotes the radius
- h denotes the height
Solution :
As we know,
- 1 cm = 1/100 m
In order to convert the value of radius of the tank from cm into m, multiply it by 1/100.
→ Radius = 70 cm
→ Radius = 70 × 1/100
→ Radius = 7/10
→ Radius = 0.7
Therefore, the radius of the tank = 0.7 m
Calculating the total surface area of cylinder :-
→ TSA = 2πr(r + h)
Substituting the given values :-
→ TSA = 2 × 22/7 × 0.7(0.7 + 1.3)
→ TSA = 2 × 22/7 × 7/10(2)
→ TSA = 2 × 22 × 1/10(2)
→ TSA = 2 × 22 × 2/10
→ TSA = 88/10
→ TSA = 8.8
Total surface area of cylinder = 8.8 m²
Therefore, the total amount of metal required to make the metal sheet = 8.8 m²