Question

An interior design working with a computer program decreases the radius of a circular rug by 10%. By what percent does the area of the circular rug decrease?
Please give an explanation on how to solve this problem, thanks!

Answer 1

Answer:

The decrease is 21%

Step-by-step explanation:

So lets say the Original area is Pi X (Radius^2)

Lets call Radius as R

For the new radius, it would be: R + 0.1R which is 1.1R

The new area is: Pi X 1.1R^2, which going further is 1.21 after squaring 1.1.

The Original area is: Pi X Radius^2

To find the percent decrease, subtract the new area by the original, cross out Pi X Radius squared and you are only left with 21%

I am in middle school so I don't know if it is going to be incorrect, but I ask you to give it a try and tell me if it was right or not. I have barely done this topic but recently I had a bonus homework question on a question almost exactly like this and this is the way I did it and I was correct. Thanks! Hope it helped! :)