A field is to be fertilized at a cost of $0.08 per square yard. the rectangular part of the field is 95 yd long and the diameter of each semicircle is 49 yd. Find the cost of fertilizing the field.

Question

Mathematics

Davin Bryan

8 October, 08:00

A field is to be fertilized at a cost of $0.08 per square yard. the rectangular part of the field is 95 yd long and the diameter of each semicircle is 49 yd. Find the cost of fertilizing the field.

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Answers (1)

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Ruby Kim · Answer 1

Assuming that this field is rectangular with 2 semi-circles (one on both ends of the field), we must first calculate the total area of the field. this is done by adding the area of the rectangular portion and the circular portion. This is done below:

Given:

Rectangular length = 95 yards

Rectangular width = semi-circle diameter = 49 yards

Area of rectangle = length * width = 95 * 49

Area of rectangle = 4655 yd^2

The area of the 2 semi-circles can be obtained by treating both as one circle.

Area of circle = pi * (d/2) ^2 = 3.1416 * (49/2) ^2

Area of circle = 1885.74 yd^2

Total area = 1885.74 + 4655 = 6540.74

We multiply the area by the cost of fertilizing:

Total cost = cost per sq. yd * total area

Total cost = 0.08 * 6540.74

Total cost = $523.26