Question

If diameter of a circle is increased by 40%, find by how much percentage its area
increases?

Answer 1

The answer is 96%

Step-by-step explanation:

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

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

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

$\bold {if \: diameter \: of \: the \: circle \: increases \: by \: 40\% \: then \: new \: diameter \: of \: the \: circle \: is \: calculated \: as \: shown \: below: }$

$\bold{that \: is \: new \: diameter = d + 0.4d = 1.4d}$

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

$\bold{new \: radius = 0.7d}$

$\bold{so,new \: area \: will \: be \: \pi(0.7d)}.$

$\therefore \bold{new\:area=\pi × 0.49d^{2}}$

$\bold {Now,we\:will\:calculate \: the \: change \: in \: area.}$

$\therefore\bold{change \: in \: area = \pi × 0.49d^{2} - \pi × \frac{d^{2}}{4}}$

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

$\therefore\bold{Change\:in\:area = 0.96 \pi \frac{d^{2}}{4}}$

$\therefore \bold{the \: area \: is \: increased \: by \: 96\%}$

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Answer 2

Answer:

Among the given options option (a) 96 % is the correct