Find the total surface area of a cylinder with a height of 10 in and width of 3 in
To find the total surface area of a cylinder, we need to add the area of the two bases to the lateral surface area.
The formula for the lateral surface area of a cylinder is:
Lateral surface area = 2 * π * r * h
The formula for the area of a circle (base of the cylinder) is:
Base area = π * r^2
Given that the height (h) is 10 in and the radius (r) is half of the width (d), which is 3 in, r = 3/2 = 1.5 in.
Plugging the values into the formulas:
Lateral surface area = 2 * π * 1.5 * 10 = 30π ≈ 94.25 in^2
Base area = π * 1.5^2 = 2.25π ≈ 7.07 in^2
Now to find the total surface area, add the lateral surface area to twice the base area:
Total surface area = 2 * base area + lateral surface area
Total surface area = 2 * 7.07 + 94.25
Total surface area ≈ 15.57 + 94.25
Total surface area ≈ 109.82 in^2
Therefore, the total surface area of the cylinder is approximately 109.82 square inches.