4. If the sum of perimeters of two circles as well
as the difference of their areas is 176
numerically, find the radii of the two circles.
Answers
Answer:
From question,
circumference of circle = Area of circle
2πr=πr2
⇒r=2
∴Radius=2 units.
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