Question

What is the surface area of this cylinder?

Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth. 10ft 10ft

Answer 1

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

\[
A = 2\pi r(h + r)
\]

where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.

In this case, you provided dimensions of 10 ft for both the height and the diameter. To find the radius, we divide the diameter by 2:

\[
r = \frac{10 \text{ ft}}{2} = 5 \text{ ft}
\]

Now, we can plug the values into the surface area formula:

1. Calculate \( h + r \):
\[
h + r = 10 \text{ ft} + 5 \text{ ft} = 15 \text{ ft}
\]

2. Substitute \( r \) and \( h + r \) into the surface area formula:
\[
A = 2 \pi r (h + r) = 2 \times 3.14 \times 5 \text{ ft} \times 15 \text{ ft}
\]

3. First, calculate \( 2 \times 3.14 \times 5 \):
\[
2 \times 3.14 = 6.28
\]
\[
6.28 \times 5 = 31.4
\]

4. Now multiply by \( 15 \):
\[
A = 31.4 \times 15 = 471
\]

Thus, the surface area of the cylinder is:

\[
A = 471 \text{ ft}^2
\]

Since the question asks to round to the nearest hundredth, the answer is:

\[
\text{Surface Area} \approx 471.00 \text{ ft}^2
\]