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The sum of radii of the two circles is 91 cm and the difference between their areas is 2002 cm2. What is the radius (in cm) of the larger circle?
- A56
- B42
- C63
- D49
Answer not set
Discussion 1
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CCommunity
Let the radii be a and b respectively
⇒ a + b = 91 ---- (1)
⇒ Difference in area = (22/7) × (a2 – b2) = 2002
⇒ a2 – b2 = 91 × 7 ---- (2)
Dividing equation 2 by equation 1 and using [a2 – b2 = (a + b) (a – b)], we get
⇒ a – b = 7 ---- (3)
By Adding equation 1 and 3, we get
⇒ 2a = 98
⇒ a = 49 cm
⇒ b = 42 cm
∴ Radii of larger circle is 49 cm
⇒ a + b = 91 ---- (1)
⇒ Difference in area = (22/7) × (a2 – b2) = 2002
⇒ a2 – b2 = 91 × 7 ---- (2)
Dividing equation 2 by equation 1 and using [a2 – b2 = (a + b) (a – b)], we get
⇒ a – b = 7 ---- (3)
By Adding equation 1 and 3, we get
⇒ 2a = 98
⇒ a = 49 cm
⇒ b = 42 cm
∴ Radii of larger circle is 49 cm