A cylinder of height 12cm and radius 5cm is made of cardboard use the value of 3.1 to calculate the total surface area of the cardboard needed to make
a) a closed cylinder.
b) a cylinder open at one end
I don't understand math lol
The surface area of a cylinder is height + 2(pi*r^2).
(pi*r^2) is the area at each end.
Is 3.1 the diameter or radius? 2r = D
I don't get it
a) To calculate the total surface area of a closed cylinder, we need to consider both the curved surface area and the area of the two circular bases.
The curved surface area of a cylinder can be calculated using the formula 2πrh, where π is approximately 3.1, r is the radius, and h is the height.
Curved surface area = 2 * 3.1 * 5 * 12
= 372 cm²
The area of each circular base can be calculated using the formula πr².
Area of each base = 3.1 * 5²
= 3.1 * 25
= 77.5 cm²
Since a closed cylinder has two bases, we need to multiply the area of one base by 2 to get the total base area.
Total base area = 2 * 77.5
= 155 cm²
Total surface area (closed cylinder) = Curved surface area + Total base area
= 372 + 155
= 527 cm²
Therefore, approximately 527 cm² of cardboard is needed to make a closed cylinder.
b) For a cylinder open at one end, we don't need to consider the area of one base since it is open. Therefore, the total surface area is equal to the curved surface area.
Total surface area (open cylinder) = Curved surface area
= 372 cm²
Therefore, approximately 372 cm² of cardboard is needed to make a cylinder open at one end.
To calculate the total surface area of the cardboard needed to make a closed cylinder, we need to find the lateral surface area and the area of the two bases.
a) Closed Cylinder:
1. Lateral Surface Area: The lateral surface area of a cylinder can be found using the formula: Lateral Surface Area = 2πrh, where π is a constant approximately equal to 3.1, r is the radius, and h is the height.
- Substituting the given values: Lateral Surface Area = 2 * 3.1 * 5 * 12 = 372 cm².
2. Base Area: The area of each base of the cylinder can be found using the formula: Base Area = πr².
- Substituting the given values: Base Area = 3.1 * 5² = 77.5 cm² (approx).
3. Total Surface Area: The total surface area can be calculated by summing up the lateral surface area and the area of the two bases.
- Total Surface Area = Lateral Surface Area + 2 * Base Area = 372 + 2 * 77.5 = 527 cm² (approx).
Therefore, the total surface area of cardboard needed to make a closed cylinder is approximately 527 cm².
b) Cylinder Open at One End:
For a cylinder open at one end, we only need to calculate the lateral surface area and the area of the one base.
1. Lateral Surface Area: The lateral surface area remains the same as in the closed cylinder case: 2 * 3.1 * 5 * 12 = 372 cm² (approx).
2. Base Area: We calculate the area of the single base using the formula: Base Area = πr².
- Substituting the given values: Base Area = 3.1 * 5² = 77.5 cm² (approx).
3. Total Surface Area: Since there is only one base, the total surface area is the sum of the lateral surface area and the area of the base.
- Total Surface Area = Lateral Surface Area + Base Area = 372 + 77.5 = 449.5 cm² (approx).
Therefore, the total surface area of cardboard needed to make a cylinder open at one end is approximately 449.5 cm².