Answer :
To find the surface area of a closed cylindrical storage tank, we need to calculate the area of both the cylindrical body and the two circular ends (top and bottom) of the tank.
Here are the step-by-step calculations:
1. Calculate the radius of the cylinder:
- Diameter of the cylinder = 2.8 meters
- Radius (r) = Diameter / 2
[tex]\[ r = \frac{2.8}{2} = 1.4 \text{ meters} \][/tex]
2. Calculate the surface area of the side (lateral surface area) of the cylinder:
- The formula for the lateral surface area of a cylinder is:
[tex]\[ \text{Lateral Surface Area} = 2 \pi r h \][/tex]
- Given: [tex]\( \pi = \frac{22}{7} \)[/tex], radius [tex]\( r = 1.4 \)[/tex] meters, and height [tex]\( h = 3 \)[/tex] meters.
[tex]\[ \text{Lateral Surface Area} = 2 \times \frac{22}{7} \times 1.4 \times 3 \][/tex]
3. Calculate the area of the two circular ends:
- The formula for the area of one circle (top or bottom) is:
[tex]\[ \text{Area of one circular end} = \pi r^2 \][/tex]
- To find the areas of both ends, we multiply by 2:
[tex]\[ \text{Total Area of two circular ends} = 2 \pi r^2 \][/tex]
- Given: [tex]\( \pi = \frac{22}{7} \)[/tex], radius [tex]\( r = 1.4 \)[/tex] meters.
[tex]\[ \text{Total Area of two circular ends} = 2 \times \frac{22}{7} \times (1.4)^2 \][/tex]
4. Sum the lateral surface area and the area of the two circular ends to get the total surface area:
[tex]\[ \text{Total Surface Area} = \text{Lateral Surface Area} + \text{Total Area of two circular ends} \][/tex]
Substituting the values, we find:
- Lateral Surface Area calculation:
[tex]\[ \text{Lateral Surface Area} = 2 \times \frac{22}{7} \times 1.4 \times 3 = 26.4 \text{ square meters} \][/tex]
- Total Area of two circular ends calculation:
[tex]\[ \text{Total Area of two circular ends} = 2 \times \frac{22}{7} \times (1.4)^2 = 12.32 \text{ square meters} \][/tex]
So, the Total Surface Area:
[tex]\[ \text{Total Surface Area} = 26.4 + 12.32 = 38.72 \text{ square meters} \][/tex]
Therefore, the surface area of the metallic sheets used to make the tank is [tex]\( 38.72 \)[/tex] square metres.
Here are the step-by-step calculations:
1. Calculate the radius of the cylinder:
- Diameter of the cylinder = 2.8 meters
- Radius (r) = Diameter / 2
[tex]\[ r = \frac{2.8}{2} = 1.4 \text{ meters} \][/tex]
2. Calculate the surface area of the side (lateral surface area) of the cylinder:
- The formula for the lateral surface area of a cylinder is:
[tex]\[ \text{Lateral Surface Area} = 2 \pi r h \][/tex]
- Given: [tex]\( \pi = \frac{22}{7} \)[/tex], radius [tex]\( r = 1.4 \)[/tex] meters, and height [tex]\( h = 3 \)[/tex] meters.
[tex]\[ \text{Lateral Surface Area} = 2 \times \frac{22}{7} \times 1.4 \times 3 \][/tex]
3. Calculate the area of the two circular ends:
- The formula for the area of one circle (top or bottom) is:
[tex]\[ \text{Area of one circular end} = \pi r^2 \][/tex]
- To find the areas of both ends, we multiply by 2:
[tex]\[ \text{Total Area of two circular ends} = 2 \pi r^2 \][/tex]
- Given: [tex]\( \pi = \frac{22}{7} \)[/tex], radius [tex]\( r = 1.4 \)[/tex] meters.
[tex]\[ \text{Total Area of two circular ends} = 2 \times \frac{22}{7} \times (1.4)^2 \][/tex]
4. Sum the lateral surface area and the area of the two circular ends to get the total surface area:
[tex]\[ \text{Total Surface Area} = \text{Lateral Surface Area} + \text{Total Area of two circular ends} \][/tex]
Substituting the values, we find:
- Lateral Surface Area calculation:
[tex]\[ \text{Lateral Surface Area} = 2 \times \frac{22}{7} \times 1.4 \times 3 = 26.4 \text{ square meters} \][/tex]
- Total Area of two circular ends calculation:
[tex]\[ \text{Total Area of two circular ends} = 2 \times \frac{22}{7} \times (1.4)^2 = 12.32 \text{ square meters} \][/tex]
So, the Total Surface Area:
[tex]\[ \text{Total Surface Area} = 26.4 + 12.32 = 38.72 \text{ square meters} \][/tex]
Therefore, the surface area of the metallic sheets used to make the tank is [tex]\( 38.72 \)[/tex] square metres.
