Shashi is painting a decorative circle on her patio. She wants the outer circle to have a diameter of 10 ft. and the inner circle to have a diameter of 7 ft. If she paints only the area between these circles, what will be the area of the painted section? Include the full value of pi in your calculation and round your answer to the nearest hundredth.(1 point) ft.2
To find the area of the painted section, we first need to find the area of both circles and then subtract the smaller circle's area from the larger one.
The formula for the area of a circle is A = πr^2, where r is the radius of the circle.
For the outer circle:
Radius = diameter / 2 = 10 ft / 2 = 5 ft
Area = π(5 ft)^2 = 25π ft^2
For the inner circle:
Radius = diameter / 2 = 7 ft / 2 = 3.5 ft
Area = π(3.5 ft)^2 = 12.25π ft^2
Therefore, the area of the painted section is:
25π ft^2 - 12.25π ft^2 = 12.75π ft^2
Rounded to the nearest hundredth, the area of the painted section is approximately 40.03 ft^2.