Use the image to answer the question.

An illustration shows a cylinder with radius, 3 meters, and perpendicular height, 9 meters. The edges that are not visible are represented by a dashed line.

Solve the surface area of the cylinder. Give both exact and approximate answers. Round the approximate answer to the nearest hundredth. Use π=3.14
.

(1 point)
Exact answer:
π m2

Approximate answer:
m2

1 answer

To calculate the surface area of a cylinder, you can use the formula:

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

Where:

  • \( r \) is the radius
  • \( h \) is the height

Given:

  • Radius \( r = 3 \) meters
  • Height \( h = 9 \) meters

Plugging in the values:

  1. Calculate the surface area using the exact formula:

\[ \text{Surface Area} = 2\pi (3)(9 + 3) = 2\pi (3)(12) = 2\pi (36) = 72\pi \ \text{m}^2 \]

Thus, the exact answer is:

\[ \text{Exact answer: } 72\pi \ \text{m}^2 \]

  1. Now, using \( \pi \approx 3.14 \) to find the approximate surface area:

\[ \text{Approximate Surface Area} = 72 \times 3.14 = 226.08 \ \text{m}^2 \]

Rounded to the nearest hundredth, the approximate answer is:

\[ \text{Approximate answer: } 226.08 \ \text{m}^2 \]

Final answers:

  • Exact answer: \( 72\pi \ \text{m}^2 \)
  • Approximate answer: \( 226.08 \ \text{m}^2 \)