What is the radius of a half circle if the area is 300?

Answer 1

This tests your ability to create an equation and manipulate it in a way so that you can make r the radius as the subject.

We know that the area of half the circle is 300.

That means the area of the full circle is 600 because 300 is half so multiply it by 2 to get the whole circle.

We know that pi x r2 is the formula for the area of a circle

So in this case:

pi x r2 = 600.

We want to find what r is so we need to rearrange the equation to make r on its own and move everything else to the other side.

We divide by pi on both sides. Doing that will cancel out the pi on the left hand side. So we will be left with

r2 = 600/pi

Let's use our calculator to find out what 600/pi is. The calculator gives 191 to 3 significant figures. So that means we have

r2 = 191

Now we need to get rid of the square on the r. To do that, we do the inverse of square which is square root. So we square root both sides. Doing that will cancel out the square on the left hand side so that we have r on its own. So:

r = sqrt191

And now we use our calculator again to work out what the square root of 191 is. We get

r = 13.8

So the radius is 13.8

Hope that helps.

Jamz159