To calculate the surface area of the given shape, we need to consider both the rectangle and the circular areas.
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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: \[ A_{\text{rectangle}} = \text{width} \times \text{height} = 30 \times 18 = 540 \text{ square yards} \]
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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: \[ A_{\text{circles}} = 2 \times 176.625 = 353.25 \text{ square yards} \]
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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.