The numerical value of the area of a circle is greater than the numerical value of its circumference. Is this statement true? Why?

It is true if the radius is greater than 2

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It is true if the radius is less than 2

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It is true if the radius is equal to 2

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It is not true if the radius is greater than 2

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Solution

The correct option is A It is true if the radius is greater than 2
$L e t t h e r a d i u s o f t h e c i r c l e b e r . T h e n i t s a r e a = π r^{2} a n d t h e c i r c u m f e r e n c e = 2 π r . ∴ \frac{a r e a o f t h e c i r c l e}{c i r c u m f e r e n c e} = \frac{π r^{2}}{2 π r} = \frac{r}{2} . N o w (i) i f r > 2, w e h a v e a r e a o f t h e c i r c l e > i t s c i r c u m f e r e n c e, (i i) i f r = 2, w e h a v e a r e a o f t h e c i r c l e = i t s c i r c u m f e r e n c e a n d (i i i) i f r < 2, w e h a v e a r e a o f t h e c i r c l e < i t s c i r c u m f e r e n c e . T h e s t a t e m e n t i s n o t a l w a s c o r r e c t . ∴ I t d e p e n d s u p o n t h e v a l u e o f r . A n s - O p t i o n A .$

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