What is the surface area of the cylinder?
Diameter: 10 inches
Height: 25 inches
The formula for the surface area of a cylinder is:
SA = 2πr² + 2πrh
where r is the radius of the base and h is the height of the cylinder.
First, we need to find the radius of the cylinder. We know that the diameter is 10 inches, so the radius is half of that:
r = 10 / 2 = 5 inches
Now we can plug in the values for r and h into the formula:
SA = 2π(5)² + 2π(5)(25)
SA = 2π(25) + 2π(125)
SA = 50π + 250π
SA = 300π
So the surface area of the cylinder is approximately 942.48 square inches (if we use π ≈ 3.14159).
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To find the surface area of a cylinder, you need to calculate the sum of the areas of the two bases and the lateral surface area.
1. Calculate the area of each base:
- The base of a cylinder is a circle, so you can use the formula for the area of a circle: A = πr^2
- The diameter is given as 10 inches, so the radius (r) is half of that: r = 10 / 2 = 5 inches
- The area of each base is A_base = π(5)^2
2. Calculate the lateral surface area:
- The lateral surface area of a cylinder is given by the formula: A_lateral = 2πrh
- The radius (r) is 5 inches, and the height (h) is given as 25 inches
- The lateral surface area is A_lateral = 2π(5)(25)
3. Calculate the total surface area:
- The total surface area is the sum of the areas of the two bases and the lateral surface area: A_total = 2A_base + A_lateral
Now, let's calculate the surface area of the cylinder:
A_base = π(5)^2 = 25π square inches
A_lateral = 2π(5)(25) = 250π square inches
A_total = 2(25π) + 250π = 50π + 250π = 300π square inches
Therefore, the surface area of the cylinder is 300π square inches.