Question

Help please it's due today. Also please leave an explanation too ty!

A square with sides 6 in is inscribed in a circle. The circumference of this circle is...
A. C = 6 * pi
B. C = 6 * square root of 2 * pi
C. C = 6 * square root of 3 * pi
D. C = 9 * pi
E. C = 36 * pi

Answer 1

B. 6π
`√(2)`

Explanation:

If you look at the help image I attached, what we are given is in RED and what we solve is in BLUE.

First, draw a diagonal in the square. Its length is the diameter, but we don't know the exact value. Since two right triangles have been created, we use Pythagorean Therom to solve for the hypotenuse/diameter:

`a^2+b^2=c^2\\6^2+6^2=c^2`

`√(36+36) =c`

`6√(2)=c`

If diameter =
`6√(2)`, then radius is
`(6√(2))/(2)` or
`3√(2)`

Circumference = 2πr

2π (
`3√(2)`)

6π
`√(2)`

I hope this helps!