A circle has the same perimeter as a square with side length 8cm. What is the circle's radius?

Question

A circle has the same perimeter as a square with side length 8cm. What is the circle's radius? Hint: Draw a diagram

Answer 1

A square with side length 8 cm has a perimeter of 32 cm  ( P = 4s ).

 

The circumference of a circle is:

   C = πd = 2πr             [you must solve for r]

 

   32 = 2πr

    16 = πr

    16/π = r         [using π=3.14 that is approximately 5.1 cm.]

 

So, if you start with a square with side length 8 cm and push each side out to make a circle, then the radius will be approximately 5.1 cm and the diameter will be approximately 10.2 cm. Try this with a 32 cm string.

Answer 2

First, let's go ahead and decode this regular English and translate it to the wonderful language of math. (cue: cheers of excitement)

 

"A circle has the same perimeter as a square" means (circle's "perimeter") = (square's perimeter)

circle's circumference = 2πr or πd, where r = radius and d = diameter. Remember that d = 2r (d is double r).

square's perimeter = 4s or s+s+s+s, where s = side

 

This brings me to...

(1) 2πr = 4s

 

"...as a square with side length 8cm." Here, we plug-in the side length, s=8.

 

(2) 2πr = 4*8 ----> 2πr = 32

 

From here, we solve by getting "r" by itself!

 

2πr/2 = 32/2 --> πr/π = (32/2)/π ---> r = 16/π ----> r = 5.0929... (don't think you'll need more than the first two digits after the decimal point)

 

In any case, the answer is either 16/π cm or 5.1 cm. Depends on how your teacher wants the answer. Hope this helps!