A cylinder has a height of 15 feet and a radius of 4 feet. Solve for the total surface area of the cylinder. Use 3.14 for π

Question

π
and round to the nearest tenth.(1 point)
Responses

301.44 feet2
301.44

feet
2
100.48 feet squared

56.52 feet2
56.52

feet
2
188.4 feet squared

477.3 feet2
477.3

feet
2
477.3 feet squared

60 feet2

Answer 1

To find the total surface area \( A \) of a cylinder, you can use the formula:

\[ A = 2\pi r^2 + 2\pi rh \]

where:

• \( r \) is the radius of the base of the cylinder,
• \( h \) is the height of the cylinder,
• \( \pi \) is approximately 3.14.

Given:

• \( r = 4 \) feet,
• \( h = 15 \) feet.

Now, substitute the values into the formula:

1. Calculate the area of the two bases: \[ 2\pi r^2 = 2 \times 3.14 \times (4^2) = 2 \times 3.14 \times 16 = 100.48 , \text{feet}^2 \]

2. Calculate the lateral surface area: \[ 2\pi rh = 2 \times 3.14 \times 4 \times 15 = 2 \times 3.14 \times 60 = 376.8 , \text{feet}^2 \]

3. Add them together to find the total surface area: \[ A = 100.48 + 376.8 = 477.28 , \text{feet}^2 \]

Rounding to the nearest tenth:

\[ A \approx 477.3 , \text{feet}^2 \]

So the total surface area of the cylinder is 477.3 feet².