Answer:
Area of the duck pond is 28.26 ft² .
Step-by-step explanation :
Formula
[tex]Area\ of\ circle = \pi r^{2}[/tex]
As given
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.
i.e the radius of the duck pond is 3 ft .
[tex]\pi = 3.14[/tex]
Putting all the values in the formula
[tex]Area\ of\ duck\ pond =3.14\times 3\times 3[/tex]
= 28.26 ft²
Therefore the area of the duck pond is 28.26 ft² .
Answer:
[tex]A = 56.55\ ft^2[/tex]
Step-by-step 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:
[tex]Area = \pi(r)^2[/tex]
where r is the radius of the circumference.
further
d = 2r
Where d is the diameter of the circumference.
Then the radius [tex]r_1[/tex] of the source is 1.5 ft.
The radius [tex]r_2[/tex] 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
[tex]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[/tex]
