Question

The radius of circle is so increased that its circumference increased by 10%.The area of the circle then increases by?

• A. 21
• B. 20
• C. 10.5
• D. 10

Answer 1

Answer:

A. 21

Solution:

Increased circumference of the circle is 10%.

Intial Circumference $= 2\pi{r_1}=100$ --------------(1)

New Circumference after increase in area $=2\pi{r_2}=110$ --------------(2)

By $(1) \div{(2)}$

$\frac{2\pi{r_1}}{2\pi{r_2}}=\frac{100}{110}$

$\frac{r_1}{r_2}=\frac{10}{11}$

Area $A_1=\pi{r^2_1}$

$A_2=\pi{r^2_2}$

$A_1=100\pi$

$A_2=121\pi$

Change in area $=121\pi-100\pi$

$=21\pi$

% increase in area $=\frac{21}{100}\times{100}$=21%