The city is putting a fountain at the entrance of the park. A scale drawing of the fountain is shown below.
Scale
1 in. : 4 ft
What is the area of the fountain in square feet?
Responses
A 4𝜋4 𝜋
B 16𝜋16 𝜋
C 64𝜋64 𝜋
D 128𝜋
Show your work
To find the area of the fountain in square feet, we need to first determine the dimensions of the fountain in inches and then convert them to feet using the given scale.
From the scale drawing, we see that the diameter of the fountain is 1 inch.
Using the scale of 1 in. : 4 ft, we can convert this to feet:
1 inch * 4 ft/inch = 4 feet
So, the diameter of the fountain in feet is 4 feet.
Next, we need to calculate the radius of the fountain:
Radius = diameter/2
Radius = 4 ft / 2
Radius = 2 ft
Now, we can find the area of the fountain:
Area = π * Radius^2
Area = π * (2 ft)^2
Area = 4π square feet
Therefore, the area of the fountain in square feet is 4π square feet.
The correct answer is A) 4𝜋.