Question

1 calculate the total surface area for the figure:
tsa =
1)
7 in
14 in

Explanation:

Step1: Recall the formula for the total surface area (TSA) of a cylinder.

The formula for the total surface area of a cylinder is \( TSA = 2\pi r^2 + 2\pi rh \), where \( r \) is the radius and \( h \) is the height of the cylinder.

Step2: Identify the values of \( r \) and \( h \) from the figure.

From the figure, the radius \( r = 7 \) inches and the height \( h = 14 \) inches.

Step3: Substitute the values of \( r \) and \( h \) into the formula.

First, calculate \( 2\pi r^2 \):
\( 2\pi r^2 = 2 \times \pi \times 7^2 = 2 \times \pi \times 49 = 98\pi \)

Next, calculate \( 2\pi rh \):
\( 2\pi rh = 2 \times \pi \times 7 \times 14 = 196\pi \)

Step4: Add the two results to get the total surface area.

\( TSA = 98\pi + 196\pi = 294\pi \)

If we use \( \pi \approx \frac{22}{7} \), then:
\( 294\pi \approx 294 \times \frac{22}{7} = 42 \times 22 = 924 \) square inches.

Answer:

The total surface area of the cylinder is \( 294\pi \) square inches (or approximately 924 square inches). If we take \( \pi \approx \frac{22}{7} \), the answer is \(\boxed{924}\) square inches.