Question

A cylinder is labeled with a height of 3 yards and a radius of 2 yards.



Find the surface area of the cylinder. Use the approximation of 3.14 for pi.
(1 point)
Responses

75.36
75.36
25.12
25.12
32.97
32.97

Answer 1

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

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

where \( r \) is the radius and \( h \) is the height. Given the radius \( r = 2 \) yards and the height \( h = 3 \) yards, we can substitute these values into the formula.

Using \( \pi \approx 3.14 \):

\[
SA = 2 \times 3.14 \times 2(3 + 2)
\]

Calculating the values step by step:

1. Calculate \( h + r = 3 + 2 = 5 \).
2. Calculate the area:

\[
SA = 2 \times 3.14 \times 2 \times 5
\]

\[
SA = 2 \times 3.14 \times 10
\]

\[
SA = 62.8
\]

Now calculate the curved surface area separately:

\[
\text{Curved Surface Area} = 2\pi rh
\]

\[
= 2 \times 3.14 \times 2 \times 3
\]

\[
= 2 \times 3.14 \times 6 = 37.68
\]

Calculate the area of the top and bottom:

\[
\text{Area of the top and bottom} = 2\pi r^2
\]

\[
= 2 \times 3.14 \times 2^2
\]

\[
= 2 \times 3.14 \times 4 = 25.12
\]

Finally, add both areas:

\[
SA = 37.68 + 25.12 = 62.8
\]

Thus, the correct calculation leads to the total surface area:

\[
\text{Surface Area} = 62.8 \text{ square yards}
\]

Since the available responses don't include 62.8, there may be a miscalculation in the options provided. Based on the calculations, the surface area derived from the dimensions provided is correct.

However, among the responses you have provided, **none match the calculated surface area of 62.8 square yards.**