Evelyn has a circular piece of fabric that is 19 inches across. She cuts a smaller circle from the fabric. The circle she removed had a 2.5 inch radius. What is the area of the remaining fabric?



Answer :

Answer:

84 [tex]\pi[/tex] inches squared

Step-by-step explanation:

To solve this, we can use the formula for area of a circle:

[tex]A = \pi r^2[/tex]

Where r equals the radius of the circle.

The large circle in this case would have a radius of 9.5 inches since the diameter is 19 inches.

[tex]A = \pi (9.5^2)\\A = 90.25\pi[/tex]

The smaller circle cut from the large circle has a radius of 2.5 inches.

[tex]A = \pi (2.5^2)\\A = 6.25\pi[/tex]

Subtract the area of the smaller circle from the large circle to get the area of the remaining fabric.

[tex]A = 90.25\pi -6.25\pi \\A = 84\pi[/tex]