RAS question
If the circumference of a circle is 44 cm, its area is (take π = 22/7):
Correct answer: (A) 154 cm².
A circle with circumference 44 cm has area 154 cm² when π is taken as 22/7.
Explanation
Use the circumference first, because it gives the radius directly: 2πr = 44. With π = 22/7, r = 44 ÷ (2 × 22/7) = 44 × 7/44 = 7 cm. Once the radius is known, apply the area formula πr². That gives (22/7) × 7² = (22/7) × 49 = 22 × 7 = 154 cm². The NCERT-linked chapter page is live and states the standard instruction used in such exercises: unless stated otherwise, take π = 22/7. With π fixed at 22/7, the arithmetic is exact within the problem’s convention.
Why the other options are wrong
- (B) 144 cm² does not follow from r = 7 cm; it would require changing the radius or the value of π after using a circumference of 44 cm.
- (C) 176 cm² is too large for a radius of 7 cm because substituting r = 7 in πr² gives 154 cm², not 176 cm².
- (D) 132 cm² is too small because it misses the computed product (22/7) × 49, which simplifies to 154 cm².
Concept
This tests mensuration linkage: using circumference to find radius, then using that radius to find area. RAS reasoning papers often repeat such questions because they check formula recall and clean fraction arithmetic in one step.