The area of a compact disc is 452 4/7 square centimeters. What is the diameter of the compact disc. Use 22/7 as an approximation for pi.

Question

 I really need help on this problem because I struggle in this and I have tried many times but I can't get it.

Answer 1

The area of a circle is πr², where r is the radius.

 

So using 22/7 for π (which I hate to do, but that's what they want), that means that for this CD:

 

452 4/7 = 22/7 * r²

 

To solve this, first we have to change the area to a common fraction instead of a mixed number.

 

452 4/7 = 452 * 7 / 7 + 4 / 7 = 3164 / 7 + 4 / 7 = 3168 / 7

 

So now we have:

 

3168 / 7 = 22/7 * r²

3168 / 7 = 22 / 7 * r²

(3168 / 7) / (22 / 7) = r²

 

144 = r²

 

so r = 12

 

Since the diameter is twice the radius, the diameter is 24 cm.