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Statement-I If the ratio of diameters of two circles $A and B$ is $7 : 5$ , then the ratio of their areas is $25 : 49$ .
$S t a t e m e n t - I I If the area of circle is 360 {cm}^{2}, then the area of sector subtending an angle of 37^{\circ} at the centre of circle is 74 {cm}^{2} .$

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Statement I is False, Statement II is False

Statement I is True, Statement II is False

Statement I is False, Statement II is True

Statement I is True, Statement II is True

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Detailed Solution

Given $\frac{d_{1}}{d_{2}} = \frac{7}{5}$

$\Rightarrow \frac{r_{1}}{r_{2}} = \frac{7}{5}$

Ratio of areas $= \frac{π r_{1}^{2}}{π r_{2}^{2}} = {(\frac{r_{1}}{r_{2}})}^{2} = {(\frac{7}{5})}^{2} = \frac{49}{25}$

Statement B:

Area of circle $= 360 c m^{2}$

$π r^{2} = 360$

$\frac{22}{7} r^{2} = 360 ° \Rightarrow r^{2} = 360 \times \frac{1}{π}$

Area of sector $= \frac{x}{360} \times π r^{2}$

$= \frac{37}{360} \times π \times \frac{360}{π}$ (False)

$= 37 c m^{2}$ .

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