Question

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

623.25 yards2
623.25 yards squared

600.53 yards2
600.53 yards squared

3,108.6 yards2
3,108.6 yards squared

1,201.05 yards2
1,201.05 yards squared
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Answer 1

To calculate the surface area of the given shape, we need to consider both the rectangle and the circular areas.

1. **Calculate the area of the rectangle:**
- The dimensions of the rectangle are given as height = 18 yards. We need the width, which isn't explicitly stated, but we can infer it from the circles.
- The diameter of the circles is 15 yards, so the radius (r) is:
\[
r = \frac{15}{2} = 7.5 \text{ yards}
\]
- The width of the rectangle can be assumed as the total diameter of two circles placed side by side:
\[
\text{Width} = 15 + 18 = 15 + 15 = 30 \text{ yards}
\]
- The area of the rectangle (A_rectangle) is:
\[
A_{\text{rectangle}} = \text{width} \times \text{height} = 30 \times 18 = 540 \text{ square yards}
\]

2. **Calculate the area of the two circles:**
- The area of one circle (A_circle) is given by the formula:
\[
A_{\text{circle}} = \pi r^2 = 3.14 \times (7.5)^2
\]
- Calculate \( (7.5)^2 \):
\[
(7.5)^2 = 56.25
\]
- Then, the area of one circle:
\[
A_{\text{circle}} = 3.14 \times 56.25 = 176.625 \text{ square yards}
\]
- Since there are two circles, the total area of both circles (A_circles) is:
\[
A_{\text{circles}} = 2 \times 176.625 = 353.25 \text{ square yards}
\]

3. **Total surface area:**
- Now, we sum the areas of the rectangle and the circles:
\[
A_{\text{total}} = A_{\text{rectangle}} + A_{\text{circles}} = 540 + 353.25 = 893.25 \text{ square yards}
\]

None of the provided options (623.25, 600.53, 3,108.6, 1,201.05) match this calculated surface area of \( 893.25 \text{ square yards}\).

It seems there might be a misunderstanding or error in the dimensions or areas provided. Please verify the dimensions again, especially the width of the rectangle or the positioning of the circles.