Question

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

Explanation:

Step1: Recall total surface area formula

The total surface area of a cylinder is the sum of the areas of the two circular bases and the lateral (curved) surface area:
$$SA = 2\pi r^2 + 2\pi r h$$
where $r = 5$ cm (radius) and $h = 8$ cm (height).

Step2: Calculate area of two bases

Substitute $r=5$ into the base area term:
$$2\pi r^2 = 2\pi (5)^2 = 2\pi \times 25 = 50\pi$$

Step3: Calculate lateral surface area

Substitute $r=5$ and $h=8$ into the lateral area term:
$$2\pi r h = 2\pi \times 5 \times 8 = 80\pi$$

Step4: Sum the two areas

Add the results from Step2 and Step3:
$$SA = 50\pi + 80\pi = 130\pi$$

Step5: Compute decimal value and round

Calculate the numerical value and round to the nearest thousandth:
$$130\pi \approx 130 \times 3.1415926536 = 408.407044968 \approx 408.407$$

Answer:

$408.407$ square centimeters