Which of the following statements are true regarding a circle of radius ‘R’?

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Solution

Q.
Which of the following statements are true regarding a circle of radius ‘R’

$(i) A r e a o f c i r c l e = π R^{2}$

$(i i) C i r c u m f e r e n c e o f c i r c l e = π R$

$(i i i) \frac{Area of circle}{Circumference of circle} = \frac{R}{2}$

$(i v) A r e a o f c i r c l e i s a l w a y s g r e a t e r t h a n i t s c i r c u m f e r e n c e$

Choose the correct option from the following:

1 (i) and (iii)

2 (ii) and (iii)

3 (iii) and (iv)

4 (i) and (iv)

Ans.
(1)

$A r e a o f c i r c l e o f r a d i u s R = π R^{2} ∴ S t a t e m e n t (i) i s c o r r e c t . C i r c u m f e r e n c e o f c i r c l e = 2 π R ∴ S t a t e m e n t (i i) i s i n c o r r e c t . A r e a o f c i r c l e = π R^{2} \frac{Area of circle}{Circumference of circle} = \frac{π R^{2}}{2 π R} = \frac{R}{2} ∴ S t a t e m e n t (i i i) i s c o r r e c t C i r c u m f e r e n c e o f c i r c l e = 2 π R L e t ’ s t a k e R = \frac{1}{2}, 2, 3 W h e n R = \frac{1}{2} A r e a = \frac{π}{4} P e r i m e t e r = π ∴ A r e a < P e r i m e t e r W h e n R = 2 A r e a = 4 π P e r i m e t e r = 4 π ∴ A r e a = P e r i m e t e r W h e n R = 3 A r e a = 9 π P e r i m e t e r = 6 π ∴ A r e a > P e r i m e t e r S o, r e l a t i o n b e t w e e n a r e a a n d p e r i m e t e r o f c i r c l e d e p e n d s u p o n i t s r a d i u s . S t a t e m e n t (i v) i s i n c o r r e c t .$

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