Question

A fountain, 3 ft in diameter, sits in the center os a circular duck pond. The pond measures 3 ft from the fountain to its edge. What is the area of the duck pond.

Answer 1

`56.55\ ft^2`

Explanation:

We know that the diameter of the fountain is 3 feet and that it is in the center of the pond.

We know that the area of a circumference is:

`\pi(r)^2`

where r is the radius of the circumference.

further

d = 2r

Where d is the diameter of the circumference.

Then the radius
`r_1` of the source is 1.5 ft.

The radius
`r_2` of the pond is 1.5 + 3 = 4.5 ft

Finally the area of the pond is equal to the area of the ring that is shown in the image

`A = \pi(r_2)^2 - \pi (r_1)^2\\\\A = \pi(4.5)^2 - \pi(1.5)^2\\\\A = \pi(4.5^2 - 1.5^2)\\\\A = 18\pi = 56.55\ ft^2`