Question

The circumference of a circle is 53.38 centimeters. What is the area in square centimeters?

Answer 1

See a solution process below:

Explanation:

To calculate the area of a circle we need to know it's radius.

The formula for the circumference of a circle is:

`C= 2pir`

Substituting `53.38"cm"` for `C` and solving for `r` gives:

`53.38"cm" = 2pir`

`53.38"cm"/color(red)(2pi) = (2pir)/(color(red)(2pi)`

`26.69/pi"cm" = (color(red)(cancel(color(black)(2pi)))r)/cancel(color(red)(2pi)`

`26.69/pi"cm" = r`

`r = 26.69/pi"cm"`

The formula for the area of a circle is;

`A = pir^2`

Substituting the radius we solved for above and calculating `A` gives:

`A = pi(26.69/pi"cm")^2`

`A = pi(712.3561/pi^2"cm"^2)`

`A = color(red)(cancel(color(black)(pi)))(712.3561/pi^color(red)(cancel(color(black)(2)))"cm"^2)`

`A = 712.3561/pi"cm"^2`

Substituting `3.14` for `pi` allows us to approximate the area as:

`A = 712.3561/3.14"cm"^2`

`A = 226.865"cm"^2`