A CYLINDER OF HEIGHT 12 CM AND RAIDUS 5CM IS MADE UP OF CARDBOARD USE THE VALUE OF 3.1 FOR PIE TO CALCULATE THE TOTAL AREA OF CARDBOARD NEEDED TO MAKE A CLOSED CYLINDER ,A CYLINDER OPENED AT ONE END.

PI, not PIE!

a = πr^2 + 2πrh
so plug in your numbers.

To calculate the total surface area of a closed cylinder, we need to consider the lateral surface area and the area of the two circular bases.

1. Lateral surface area: The formula to calculate the lateral surface area of a cylinder is given by 2 x π x radius x height. In this case, the radius is 5 cm and the height is 12 cm. Using the value of π as 3.1, we can substitute the values into the formula:
Lateral surface area = 2 x 3.1 x 5 cm x 12 cm
= 372 cm²

2. Circular base area: The formula to calculate the area of a circle is π x radius². Since the cylinder has two circular bases, we need to calculate the area of one base and double it. The radius is 5 cm. Substituting the value of π as 3.1, we can calculate the area of one base:
Circular base area = 3.1 x (5 cm)²
= 3.1 x 25 cm²
= 77.5 cm²

To find the total area of cardboard needed for the closed cylinder, we add the lateral surface area and the area of the two circular bases:
Total surface area = Lateral surface area + 2 x Circular base area
= 372 cm² + 2 x 77.5 cm²
= 372 cm² + 155 cm²
= 527 cm²

Now let's calculate the total area of cardboard needed for a cylinder opened at one end:

For a cylinder opened at one end, we only need to consider the lateral surface area and the area of the one circular base.

1. Lateral surface area: The formula remains the same as for the closed cylinder: 2 x π x radius x height. Using the same values as before, we can calculate the lateral surface area:
Lateral surface area = 2 x 3.1 x 5 cm x 12 cm
= 372 cm²

2. Circular base area: The formula is the same as before: π x radius². We can calculate the area of one base:
Circular base area = 3.1 x (5 cm)²
= 3.1 x 25 cm²
= 77.5 cm²

To find the total area of cardboard needed for the cylinder opened at one end, we add the lateral surface area and the area of the one circular base:
Total surface area = Lateral surface area + Circular base area
= 372 cm² + 77.5 cm²
= 449.5 cm²

Therefore, to make a closed cylinder, we would need 527 cm² of cardboard, and to make a cylinder opened at one end, we would need 449.5 cm² of cardboard.

To calculate the total surface area of a closed cylinder, you need to find the area of the curved surface (lateral area) and the area of the two bases.

1. Curved surface area of the closed cylinder:
The curved surface area of a cylinder can be calculated using the formula:

C.S.A = 2 * π * radius * height

Given that the height is 12 cm and the radius is 5 cm, substitute these values into the formula:

C.S.A = 2 * 3.14 * 5 * 12
≈ 376.8 cm²

2. Area of the bases:
The area of each base of a cylinder is given by the formula:

Base area = π * radius²

Given the radius is 5 cm, calculate the base area:

Base area = 3.14 * 5²
= 3.14 * 25
≈ 78.5 cm²

Since there are two bases, the total area of the bases is:

Total base area = 2 * 78.5
= 157 cm²

3. Total surface area of the closed cylinder:
To find the total surface area, add the curved surface area and the total base area:

Total surface area = C.S.A + Total base area
= 376.8 + 157
= 533.8 cm²

Therefore, the total area of cardboard needed to make a closed cylinder is approximately 533.8 cm².

Now, to calculate the total surface area of a cylinder open at one end, you just need to subtract the area of one base:

Total surface area of open cylinder = C.S.A + Base area
= 376.8 + 78.5
= 455.3 cm²

Hence, the total area of cardboard needed to make a cylinder open at one end is approximately 455.3 cm².

answer