 # If diameter of a circle is increased by 40%, Question:

If diameter of a circle is increased by 40%, then its area increase by

(a) 96%

(b) 40%

(c) 80%

(d) 48%

Solution:

If $d$ is the original diameter of the circle, then the original radius is $\frac{d}{2}$.

$\therefore$ area of the circle $=\pi\left(\frac{d}{2}\right)^{2}$

$\therefore$ area of the circle $=\pi \times \frac{d^{2}}{4}$

If diameter of the circle increases by 40%, then new diameter of the circle is calculated as shown below,

That is new diameter $=d+0.4 d$

$=1.4 d$

$\therefore$ new radius $=\frac{1.4 d}{2}$

$\therefore$ new radius $=0.7 d$

So, new area will be $\pi(0.7 d)^{2}$.

$\therefore$ New area $=\pi \times 0.49 d^{2}$

Now we will calculate the change in area.

$\therefore$ change in area $=\pi \times 0,49 d^{2}-\pi \times \frac{d^{2}}{4}$

$\therefore$ change in area $=\left(0.49-\frac{1}{4}\right) \pi d^{2}$

$\therefore$ change in area $=0.96 \pi \frac{d^{2}}{4}$

Therefore, its area is increased by $96 \%$.

Hence, the correct answer is option (a).