Question

Preston measured the button on his shirt. Then he calculated that it has an area of 50.24 square millimeters. What is the button's diameter?

Answer 1

*note: for this problem you have to round a few values. I rounded to 2 decimal places, but your answer could be different if you have to round to more/less than 2 decimal places

Answer: Diameter = 8 millimeters


Buttons are circles, so we will use the formula for area of a circle:

A = πr^2

We are solving for the diameter, which is 2 times the radius:

d = 2r

So now we plug in what we know.
The area A = 50.24 square millimeters, therefore we plug it in and simplify:

50.24 square millimeters = πr^2

50.24/π = r^2

15.99 = r^2

squareroot(15.99) = r

r = 4 millimeters

Now we use the radius to calculate the diameter.

r = 4 millimeters

d = 2r

d = 2(4)

diameter = 8 millimeters