36π is the surface area of the given cylinder.
To find the surface area of a cylinder, you need to calculate the areas of the two circular bases and the lateral surface area.
The formula for the surface area of a cylinder is:
Surface Area = 2πr² + 2πrh
Given:
Height (h) = 7
Radius (r) = 2
First, let's calculate the area of each circular base:
Area of a circular base = πr²
Area of the top circular base = π(2²) = 4π
Area of the bottom circular base = π(2²) = 4π
Next, let's calculate the lateral surface area:
Lateral surface area = 2πrh
Lateral surface area = 2π(2)(7) = 28π
Now, we can find the total surface area by adding the areas of the bases and the lateral surface area:
Total Surface Area = Area of top base + Area of bottom base + Lateral surface area
Total Surface Area = 4π + 4π + 28π = 36π
Therefore, the surface area of the cylinder with a height of 7 and a radius of 2 is 36π.
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