Question

find the surface area of a cylinder with a base diameter of 10 cm and a height of 9 cm. use the value 3.14 for π, and do not do any rounding. be sure to include the correct unit.

Explanation:

Step1: Find the radius

The diameter is 10 cm, so the radius \( r=\frac{10}{2} = 5 \) cm.

Step2: Recall the formula for the surface area of a cylinder

The surface area of a cylinder is given by \( SA = 2\pi r^{2}+2\pi rh \), where \( r \) is the radius and \( h \) is the height.

Step3: Calculate the area of the two circular bases

For the two bases, \( 2\pi r^{2}=2\times3.14\times5^{2}=2\times3.14\times25 = 157 \) \( cm^{2} \).

Step4: Calculate the lateral (curved) surface area

The lateral surface area is \( 2\pi rh=2\times3.14\times5\times9 = 282.6 \) \( cm^{2} \).

Step5: Find the total surface area

Add the area of the two bases and the lateral surface area: \( SA=157 + 282.6=439.6 \) \( cm^{2} \).

Answer:

\( 439.6 \) square centimeters (or \( 439.6\space cm^{2} \))