Question

If the radius of a circle is increased by 10 % then the area is increased by,

Answer 1

\(\pi r^2\)

\(\pi (r*1.1)^{2} = 1.21\cdot\pi r^{2}\)

What do you think?

Answer 2

@hartnn Yeah lol ? It is a circle but it is a very diff ques..

Answer 3

@tkhunny You are welcome to provide hints and explain

Answer 4

Already did.

Radius increased by 10% -- r*1.1
Area is increased by ???

Answer 5

Please explain how did you do the first step

Answer 6

Area of a Circle = \(\pi r^{2}\), given the radius.
That's the first step.

Answer 7

I know that the Area of a circle = pi r^2

Answer 8

New Radius is 10% greater than old radius. R = r*1.1
Area of new circle: \(\pi R^{2}\).

Answer 9

Got it what next ?

Answer 10

Raio of New Area to Old Area \(\dfrac{\pi R^{2}}{\pi r^{2}}\).

Answer 11

Ratio*

Answer 12

*Ratio - right

A little algebra \(\dfrac{\pi R^{2}}{\pi r^{2}} = \dfrac{R^{2}}{r^{2}} = \dfrac{(1.1\cdot r)^{2}}{r^{2}} = \dfrac{1.1^{2}r^{2}}{r^{2}} = 1.1^{2} = 1.21\)

And we see a 21% increase!

Answer 13

Thank you.