1. ## Area word problem

when mineral deposits formed a coating 1 mm thick on the inside of a pipe, the area through which fluid can flow was reduced by 20%. Find the original inside diameter.
area of circle = pi(r^2) diameter 2r

2. Originally Posted by lightstevoo
when mineral deposits formed a coating 1 mm thick on the inside of a pipe, the area through which fluid can flow was reduced by 20%. Find the original inside diameter.
area of circle = pi(r^2) diameter 2r

we just need to find $\displaystyle r$, then multiply it by 2 to find the diameter $\displaystyle D = 2r$.

The original area is $\displaystyle A_1 = \pi r^2$

When the radius is decreased by 1mm, the area is $\displaystyle A_2 = \pi (r - 1)^2$

But that is 20% of $\displaystyle A_1$. Thus we have

$\displaystyle A_2 = 0.2A_1$

$\displaystyle \Rightarrow \pi (r - 1)^2 = 0.2 \pi r^2$

Now solve for $\displaystyle r$ so you can answer the problem