Question

Surface Area of Cylinders Quick Check
1 of 51 of 5 Items
Question
Use the image to answer the question.

An illustration shows a horizontal rectangle of height 18 yards with a circle of diameter 15 yards attached to its top left and a circle of diameter 15 yards attached to its bottom right.

Calculate the surface area. Use 3.14 for π
.

(1 point)
Responses

3,108.6 yards2
3,108.6 yards squared

600.53 yards2
600.53 yards squared

1,201.05 yards2
1,201.05 yards squared

623.25 yards2

Answer 1

To calculate the surface area of the cylinder described in your question, we can use the formula for the surface area of a cylinder:

\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]

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

Given:
- The diameter of the circles is 15 yards, therefore the radius \(r\) is half of that:
\[
r = \frac{15}{2} = 7.5 \text{ yards}
\]
- The height of the cylinder \(h\) is 18 yards.

Now we can plug the values into the formula:

1. Calculate \(2\pi r^2\):
\[
2\pi r^2 = 2 \times 3.14 \times (7.5)^2
\]
First calculate \(r^2\):
\[
(7.5)^2 = 56.25
\]
Now substitute:
\[
2\pi r^2 = 2 \times 3.14 \times 56.25 \approx 352.5
\]

2. Calculate \(2\pi rh\):
\[
2\pi rh = 2 \times 3.14 \times 7.5 \times 18
\]
First calculate \(rh\):
\[
7.5 \times 18 = 135
\]
Now substitute:
\[
2\pi rh = 2 \times 3.14 \times 135 \approx 847.2
\]

3. Now add both components to find the total surface area:
\[
\text{Surface Area} = 352.5 + 847.2 \approx 1199.7 \text{ square yards}
\]

Comparing the total with the options available, it looks like the closest match is **1,201.05 yards²**.

**Answer: 1,201.05 yards²**.