What is the surface area of the cylinder with height 8 cm and radius 5 cm ? Round your answer to the nearest thousandth.

Question

UpStudy AI · Accepted Answer

The surface area $$ S $$ of a cylinder can be calculated with the formula:
$$
S = 2\pi r^2 + 2\pi r h
$$

Given:
- $$ r = 5 \, \text{cm} $$
- $$ h = 8 \, \text{cm} $$

**Step 1: Calculate the area of the two circular bases.**

$$
2\pi r^2 = 2\pi (5)^2 = 2\pi (25) = 50\pi
$$

**Step 2: Calculate the lateral surface area.**

$$
2\pi r h = 2\pi (5)(8) = 80\pi
$$

**Step 3: Add the areas to get the total surface area.**

$$
S = 50\pi + 80\pi = 130\pi
$$

**Step 4: Convert the surface area to a decimal and round to the nearest thousandth.**

$$
S \approx 130 \times 3.141593 \approx 408.407
$$

The surface area of the cylinder is approximately $$ 408.407 \, \text{cm}^2 $$.
The surface area of the cylinder is approximately 408.407 cm².

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