Question

33. The difference of areas of two concentric circles is 770cm? and the difference of their radiſ is 7cm. Find
the radius of each circle​

Answer 1

Given :

The difference of areas of two concentric circles is 770cm² and the difference of their radii is 7cm.

To find :

• Radius of each circle

Solution :

Two concentric circles are in the form of ring. They have two circles i.e inner & outer

• Consider outer radius be R & inner radius be r

★ Difference of radii of concentric circles is 7cm

→ R - r = 7

→ R = 7 + r ---(i)

★ Difference of areas of two concentric circles is 770cm²

→ Area of outer circle - Area of inner circle = 770

→ πR² - πr² = 770

• Take π as a common

→ π(R² - r²) = 770

• Apply identity
• a² - b² = (a + b)(a - c)

→ π(R + r)(R - r) = 770

• Put the value of 'R'

→ π[(7+r)+r][(7+r) - r] = 770

→ π(7 + r + r)(7 + r - r) = 770

→ 7π(7 + 2r) = 770

→ 7 × 22/7(7 + 2r) = 770

→ 22(7 + 2r) = 770

→ 7 + 2r = 770/22

→ 7 + 2r = 35

→ 2r = 35 - 7

→ 2r = 28

→ r = 28/2

→ r = 14 cm

•°• Internal radius (r) = 14 cm

→ External radius

→ R = 7 + r (From i)

→ R = 7 + 14

→ R = 21 cm

•°• External radius (R) = 21 cm

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Answer 2

Given :-

Difference of areas of two circle = 770 cm

Difference of radii = 7 cm

To Find :-

Radius of both circle

Solution :-

Let the radii be R and r

$\tt R - r = 7$

Therefore,

πR² - πr² = 770

$\sf \pi (R^{2}- r^{2}) = 770$

π(R + r)(R - r) = 770

π(7 + r + r)(7 + r - r) = 770

$\sf 22(7 + 2r) = 770$

$\sf 22 \times 7 + 44r = 770$

$\sf 154 + 44r = 770$

$\sf 770 - 154 = 14r$

$\sf 616 = 14r$

r = 14 cm

Radii of other circle = R

R = 14 + 7

R = 21 cm