Question

What is the radius of a circle with an area of 706.95 centimeters cubed?

Answer 1

See a solution process below:

Note: Assuming the area of the circle is 706.95 cm squared not cm cubed.

Explanation:

The formula for the area of a circle is:

`A_c = pir^2`

Where:

`A_c` is the area of the circle": `706.95"cm"^2` for this problem.

`pi` is a constant: We can estimate `pi` as `3.142` for this problem.

`r` is the radius of the circle: What we are solving for in this problem.

Substituting and solving for `r` gives:

`706.95"cm"^2 = 3.142r^2`

`(706.95"cm"^2)/color(red)(3.142) = (3.142r^2)/color(red)(3.142)`

`225"cm"^2 = (color(red)(cancel(color(black)(3.142)))r^2)/cancel(color(red)(3.142))`

`225"cm"^2 = r^2`

`sqrt(225"cm"^2) = sqrt(r^2)`

`15"cm" = r`

`r = 15"cm"`

The radius of the circle is approximately 15 centimeters