Question

find the total surface area of the cylinder. sa =? cm² round to the nearest hundredth. use 3.14 for π

Explanation:

Step1: Recall the formula for the surface area of a cylinder.

The formula for the total surface area of a cylinder is \( SA = 2\pi r^2 + 2\pi rh \), where \( r \) is the radius and \( h \) is the height. From the diagram, the radius \( r = 5 \) cm and the height \( h = 5 \) cm. We use \( \pi = 3.14 \).

Step2: Calculate the area of the two circular bases.

The area of one circular base is \( \pi r^2 \), so for two bases, it is \( 2\pi r^2 \). Substituting \( r = 5 \) and \( \pi = 3.14 \):
\( 2\times3.14\times5^2 = 2\times3.14\times25 = 157 \)

Step3: Calculate the lateral (curved) surface area.

The lateral surface area is \( 2\pi rh \). Substituting \( r = 5 \), \( h = 5 \), and \( \pi = 3.14 \):
\( 2\times3.14\times5\times5 = 157 \)

Step4: Sum the two areas to get the total surface area.

Add the area of the two bases and the lateral surface area: \( SA = 157 + 157 = 314 \)

Answer:

\( 314.00 \) (since we round to the nearest hundredth, and 314 is already a whole number, we can write it as 314.00)