Question

Find the radius of a circle with the given circumference. 6 square root of 2 pi in.

Answer 1

To find the circle's radius from the given circumference of 6√2π inches, we divide the circumference by 2π and simplify, resulting in a radius of 3√2 inches.

Step-by-step explanation:

Finding the Radius from Circumference

The student is asking to find the radius of a circle given its circumference. The circumference (C) of a circle is given by the formula C = 2πr, where r is the radius of the circle. The number π (pi) is approximately 3.14159. If we have a circumference of 6√2π inches, we can solve for r by dividing the circumference by 2π.

First, let's set up our equation with the given circumference:

C = 2πr = 6√2π

To find the radius, r, we divide both sides of the equation by 2π:

r = \frac{6√2π}{2π}

Now, simplify by canceling out the π from numerator and denominator:

r = \frac{6√2}{2}

And then simplifying further:

r = 3√2 inches

This means the radius of the circle is 3√2 inches.

Answer 2

`A_(circle) = \pi r^2`


`r^2 = (A)/(\pi)`


`r = \sqrt{(A)/(\pi)}`


`r = \sqrt{(6√(2)\pi)/(\pi)}`


`r = \sqrt{6√(2)}`