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Formula for calculating the lateral surface area of a cylinder
Sxq = 2πrh
Formula for calculating the area of the two circular bases
S2đ = 2πr^2
The formula for calculating the total surface area of a cylinder is:
S = 2πr^2 + 2πrh = 2πr(r + h)
Where:
- Sxq is the lateral surface area of the cylinder.
- S2đ is the area of the two circular bases of the cylinder.
- Stp is the total surface area of the cylinder.
- π is the mathematical constant π = 3.14159265359
- r is the radius of the circular base.
- h is the height of the cylinder.
Method for calculating the total surface area of a cylinder
To calculate the total surface area of a cylinder, you can calculate the area of the two circular bases and the lateral surface area separately, then sum them up to get the total surface area:
1. Firstly, calculate the area of the circular base of the cylinder using the formula:
Sd = πr^2
If you know the radius r, simply apply the formula. If the radius r is unknown, you need to find r based on the data. Then, calculate the area of the circular base of the cylinder.
2. Next, calculate the lateral surface area of the cylinder:
The formula for calculating the lateral surface area of a cylinder is:
Typically, the height will be given. With the radius r known from step 1, you can easily calculate the lateral surface area of the cylinder.
3. Finally, apply the formula to calculate the total surface area of the cylinder:
Stp = 2.Sd + Sxq
Alternatively, you can find the radius r and height h from the given requirements and then directly apply the formula to calculate the total surface area of the cylinder:
Stp = 2πr^2 + 2πrh = 2πr(r + h)
Example
Example 1: Calculate the total surface area of a cylinder with the length of the circular base as 10cm and the distance between the two bases as 6cm.
Solution
According to the problem, we have: h = 6cm; 2r = 10cm => r = 5cm.
Applying the formula to calculate the total surface area of the cylinder:
Stp = 2πr(r + h) = 2π.5(5 + 6) = 110π(cm^2)
=> Therefore, the total surface area of the cylinder is 110π(cm^2)
Example 2: Calculate the total surface area of a cylinder with a height of 7cm and a lateral surface area of 310 (cm^2)
Solution:
According to the problem, we have: h = 7; Sxq = 310
Applying the formula to calculate the lateral surface area Sxq = 2πrh
=> r = (Sxq) / (2πrh) ≈ 7cm
So,
Total surface area of the cylinder: Stp=618cm2
Above is the article sharing the formula and specific examples of calculating the total surface area of a cylinder. Hopefully, the article will help you understand more about how to calculate the total surface area of a cylinder for specific problems. Good luck!
