Two concentric circles with radii p cm and (p + 2) cm are drawn on a p

1.	Two concentric circles with radii p cm and (p + 2) cm are drawn on a paper. The difference between their areas is 44 sq.cm What is the value of p?(Take π = 22/7)1. 1.52. 53. 64. 2.5
Answer» Correct Answer - Option 4 : 2.5 Given: Radius of First circle = p cm Radius of Second circle = (p + 2) cm Difference between areas of both the circles = 44 cm² Formula Used: Area of circle = π(Radius)² (a + b)² = a² + b² + 2ab Calculation: Area of First circle = π(p cm)² ⇒ πp² cm² Area of Second circle = π{(p + 2) cm}² ⇒ π(p² + 4p + 4) cm² Difference between area of both the circles = π(p2 + 4p + 4) – πp2 ⇒ π(p2 + 4p + 4 – p²) = 44 ⇒ 4π(p + 1) = 44 ⇒ 4 × (22/7)(p + 1) = 44 ⇒ p + 1 = (44 × 7)/88 ⇒ p + 1 = 7/2 ⇒ p = 7/2 – 1 ⇒ p = 5/2 ⇒ p = 2.5 ∴ The value of p is 2.5

Two concentric circles with radii p cm and (p + 2) cm are drawn on a paper. The difference between their areas is 44 sq.cm What is the value of p?(Take π = 22/7)1. 1.52. 53. 64. 2.5

Answer» Correct Answer - Option 4 : 2.5

Given:

Radius of First circle = p cm

Radius of Second circle = (p + 2) cm

Difference between areas of both the circles = 44 cm²

Formula Used:

Area of circle = π(Radius)²

(a + b)² = a² + b² + 2ab

Calculation:

Area of First circle = π(p cm)²

⇒ πp² cm²

Area of Second circle = π{(p + 2) cm}²

⇒ π(p² + 4p + 4) cm²

Difference between area of both the circles = π(p2 + 4p + 4) – πp2

⇒ π(p2 + 4p + 4 – p²) = 44

⇒ 4π(p + 1) = 44

⇒ 4 × (22/7)(p + 1) = 44

⇒ p + 1 = (44 × 7)/88

⇒ p + 1 = 7/2

⇒ p = 7/2 – 1

⇒ p = 5/2

⇒ p = 2.5

∴ The value of p is 2.5

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