# Thread: Circular Plot

1. ## Circular Plot

The circumference of a circular plot of land is increased by 10%. What is the best estimate of the total percentage that the area of the plot increased?
(1) 10% (3) 25%
(2) 21% (4) 31%

The answer is 21%. I have no idea how to even start this question.

I know that A = pi(r^2) and C = pi(d)

This question makes no sense to me.

2. Originally Posted by magentarita
The circumference of a circular plot of land is increased by 10%. What is the best estimate of the total percentage that the area of the plot increased?
(1) 10% (3) 25%
(2) 21% (4) 31%

The answer is 21%. I have no idea how to even start this question.

I know that A = pi(r^2) and C = pi(d)

This question makes no sense to me.

well, if the circumference increases by 10% it means the radius increases by that amount, right? so $\displaystyle r \to 1.1r$

now $\displaystyle A = \pi r^2$

let $\displaystyle r \to 1.1r$

then $\displaystyle A \to \pi (1.1r)^2 = 1.21 \pi r^2$

so $\displaystyle A \to 1.21 A$. in other words, it increases by 21%

3. ## great

Originally Posted by Jhevon
well, if the circumference increases by 10% it means the radius increases by that amount, right? so $\displaystyle r \to 1.1r$

now $\displaystyle A = \pi r^2$

let $\displaystyle r \to 1.1r$

then $\displaystyle A \to \pi (1.1r)^2 = 1.21 \pi r^2$

so $\displaystyle A \to 1.21 A$. in other words, it increases by 21%
A great reply.

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### The circumference of circle plot of land is increased by 10% . What is the best estimate of the total percentage that area of the plot increased .

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