Question

The area of a compact disc is 78.53 square centimeters. What is the radius of the disc? Use pi = 3.14​

Answer 1

`\boxed {\boxed {\sf About \ 5 \ centimeters }}`

Explanation:

The area of a circle is found using this formula:

`a= \pi r^2`

We know the area of the disc is 78.53 square centimeters and 3.14 is being used for pi.

`78.53 \ cm^2 = (3.14) r^2`

We are solving for the radius, so we must isolate the variable r.

3.14 and r² are being multiplied. The inverse of multiplication is division, so divide both sides by 3.14

`(78.53 \ cm^2)/(3.14) = ((3.14) r^2)/(3.14)`

`(78.53 \ cm^2)/(3.14) =r^2`

`25.0095541 \ cm^2 = r^2`

r is being squared, so we must take the square root of both sides.

`√(25.0095541 \ cm^2) = \sqrt {r^2}`

`√(25.0095541 \ cm^2) = r`

`5.00095532 \ cm = r \\5 \ cm \approx r`

The radius of the disc is about 5 centimeters.