Maths / Comparing Quantities / Percentage Change

QUESTION

If redius of a circle is increased by 100% then area of the circle will be increased by

 OPTIONS A. 200% B. 100% C. 300% D. 400%
Right Option : C

EXPLANATION
Explain TypeExplanation Content
Text

$100X2=200\\\\(+)10.0\:\:\:\:10.0=\frac{100}{300}$

increase = 100% of r=1.0r

$\dpi{120} \fn_jvn \large Original\: Area = \pi X r^2$

$\dpi{120} \large \dpi{120} \large \dpi{120} \fn_jvn \large New\: Area = \pi X (2r)^2 = 4 \pi Xr^2$

$\dpi{120} \fn_jvn \large Increase= 4 \pi Xr^2 -\pi X r^2 = 3 \pi r^2$

$\dpi{120} \large Percentage \: Increase= \frac{increase}{original}X 100=\frac{3 \pi r^2}{\pi r^2} X 100=300$

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