Question

Nicholas has a map that shows a rectangular park with a circular pond. The scale of the map is 1.5 in: 8 yd. On a map, the width of the park is 2.5 inches and the length is 6.25 inches. The pond has a diameter of 2 inches. Find the actual area of the circular pond.Use the pi key. (Answer to the nearest tenth.)

Answer 1

The actual area of the pond is 88.9 yd^2

Explanation:

We know that in the map, 1.5 inches are equivalent to 8 yards in the real park.

We know that in the map, the pond has a diameter of 2 inches.

Now we want to find the actual area of the circular pond.

Then the first step is to find the diameter of the real pond.

We know that:

1.5 in = 8 yd.

Now we need to count how many times we have 1.5 inches in the diameter of the pond in the map, this is:

N = 2 in/ 1.5in = 1.33

Then the actual diameter of the pond is 1.33 times 8 yards, this is:

D = 1.33*8yd = 10.64 yd

Now, we know that for a circle of diameter d, the area is:

A = pi*(d/2)^2

where pi = 3.14

Then the area of the pond is:

A = 3.14*(10.64 yd/2)^2 = 88.9 yd^2