Question

Find the surface area of a cylinder with a height of 3.2 m and a radius of 1.2 m. Round your answer to the nearest hundredth.(1 point)
Responses

12.06 m2
12.06 m2

84.40 m2
84.40 m2

33.16 m2
33.16 m2

24.12 m2

Answer 1

To find the surface area of a cylinder, we can use the following formula:

\[
\text{Surface Area} = 2\pi r(h + r)
\]

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

Given:
- \( r = 1.2 \) m,
- \( h = 3.2 \) m,

Now, substitute the values into the formula:

\[
\text{Surface Area} = 2\pi (1.2) (3.2 + 1.2)
\]
\[
= 2\pi (1.2)(4.4)
\]
\[
= 2\pi (5.28)
\]
\[
= 10.56\pi
\]

Now, plugging in \( \pi \approx 3.14 \):

\[
10.56 \times 3.14 \approx 33.18 \text{ m}^2
\]

Rounding to the nearest hundredth, the surface area of the cylinder is approximately:

\[
\text{Surface Area} \approx 33.18 \text{ m}^2
\]

Among the given responses, the closest result is:

**33.16 m²**.