4. If the sum of perimeters of two circles as well
as the difference of their areas is 176
numerically, find the radii o

2 thoughts on “4. If the sum of perimeters of two circles as well<br />as the difference of their areas is 176<br />numerically, find the radii o”

1. Answer:

   From question,

   circumference of circle = Area of circle

   2πr=πr2

   ⇒r=2

   ∴Radius=2 units.

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2. Answer:

   r₁= 28.5 and r₂= 27.5

   Step-by-step explanation:

   Let radius of circle 1 be r₁

   Let radius of circle 2 be r₂

   Perimeter i.e., circumference of two circles = πr₁ + πr₂

   Difference of their area = π(r₁)² – π(r₂)²

   Given,

   Sum of perimeters = Difference of their areas = 176

   ∴ πr₁ + πr₂ = π(r₁)² – π(r₂)² = 176

   ∴ πr₁ + πr₂ = 176

   ∴ π (r₁ + r₂) = 176

   ∴ r₁ + r₂ = 176 / π

   ∴ r₂ = 56 – r₁ ———————- (a)

   π(r₁)² – π(r₂)² = 176

   ∴ π[ (r₁)²- (r₂)² ] = 176

   ∴ π [ (r₁)² – (56-r₁)² ] = 176—————-( from (a) )

   ∴ π [ r₁² – (56²- 112r₁-r₁²) = 176

   ∴ r₁² – 3136 + 112r₁ + r₁² = 176 / π

   ∴ 112r₁ – 3136 = 56

   ∴ 112r₁ = 56 + 3136 = 3192

   ∴ 112r₁ = 3192

   ∴ r₁ = 3192 / 112 = 28.5

   Substituting this value in (a)

   ∴ r₂ = 56 – r₁

   ∴ r₂ = 56 – 28.5 = 27.5

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