Question

three concentric circles of radius 10 cm 5 cm and X is greater than 10 is greater than 5 if the area enclosed by circle X cm and 10cm is same as the area enclosed by circles with 10 cm and 5 cm. find the area of the largest circle

Answer 1

π(x^2 - 10^2) = π(10^2 - 5^2)

x^2 - 10^2 = 10^2 - 5^2

x^2 = 10^2 + 10^2 - 5^2

x^2 = 175

X = root(175) = 5 root 7

Answer 2

I think according to 1st condition, the second shall be - "if the area enclosed by circle X cm and 10cm is same as the area of circles with 10 cm and 5 cm......."
If so then,

Given That:
X>10>5
Area enclosed by circle of xcm & 10cm = Area of circle with 10cm & 5cm

Solution:
According to the given conditions, we get
(π/4)×(X^2 - 10^2) = (π/4)×(10^2 + 5^2)
Therefore, (X^2 - 10^2) = (10^2 + 5^2)
or x^2 = 125 + 100
or x = √225
Therefore, x = 15 cm

Now the area of largest circle = (π/4) × 15^2
= 0.7854 × 225 = 176.71 cm^2

Hence, the area of largest circle = 176.71 cm^2