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Question

A cylinder is labeled with a height of 13 and radius of 5.

Find the surface area of the cylinder. Use the approximation of 3.14 for pi.

Answer 1

To find the surface area of the cylinder, we need to calculate the sum of the areas of its two bases and the lateral surface.

The area of a base of a cylinder is given by the formula:
Area of a base = π * radius^2

Using the given radius of 5, we can calculate the area of one base:
Area of one base = 3.14 * 5^2 = 3.14 * 25 = 78.5

Since a cylinder has two bases, the total area of both bases is:
Total base area = 2 * 78.5 = 157

The lateral surface area of a cylinder is given by the formula:
Lateral surface area = 2 * π * radius * height

Using the given height of 13 and radius of 5, we can calculate the lateral surface area:
Lateral surface area = 2 * 3.14 * 5 * 13 = 2 * 3.14 * 65 = 408.4

Therefore, the surface area of the cylinder is the sum of the base area and the lateral surface area:
Surface area = Total base area + Lateral surface area = 157 + 408.4 = 565.4

The surface area of the cylinder is approximately 565.4.