Sunday, May 27, 2018

Tricks Development

Prabhakar T 9:03 AM

Q. Radius of a circle is increased by 10 %, find the percentage increase in area.

Ans. You can get the answer by using the formula below:

Percentage increase in the area = $\small 2m + \frac{m^{2}}{100}$

Percentage increase in the area = $\small 2\times 10 + \frac{100}{100}$

Percentage increase in the area = 21

The answer is 21.

But how do I get the formula?

Let me explain below.

Area of a circle = A= $\pi r^{2}$

Suppose the radius is increased m%

New Area = $\pi \times \left ( r + \frac{rm}{100} \right )^{2}$

New Area =   $\pi \times \left ( \frac{100r+rm}{100} \right )^{2}$

New Area =   $\pi \times \left ( \frac{10000r^{2}+200r^{2}m+r^2{m^{2}}}{10000} \right )$

New Area =    $\frac{10000\pi r^{2}+200\pi r^{2}m+\pi r^{2}m^{2}}{10000}$

Increase in the area = New Area – Original Area

Increase in the area = $\frac{10000\pi r^{2}+200\pi r^{2}m+\pi r^{2}m^{2}}{10000}$ – $\pi r^{2}$

Increase in the area = $\frac{200\pi r^{2}m+\pi r^{2}m^{2}}{10000}$

Percentage increase in the area = Increase X 100
Orignal

Percentage increase in the area = $\frac{\frac{200\pi r^{2}m+\pi r^{2}m^{2}}{10000}}{\pi r^{2}} \times 100$

Percentage increase in the area = $2m + \frac{m^{2}}{100}$