Question

the sum of the radii of two circle is 84 cm and the difference of their areas is 5544
CM calculate the radii of two circles​

Answer 1

Answer:

your answer is

52.5 cm ,

31.5 cm

Answer 2

Step-by-step explanation:

Given:-

The sum of the radii of two circle is 84 cm and the difference of their areas is 5544 cm.

To find :-

Calculate the radii of two circles ?

Solution :-

Let the radius of the first circle be R cm

Let the radius of the second circle be r cm

Let R > r

Area of th first circle = πR² sq.cm

Area of the second circle = πr² sq.cm

Given that

The sum of the radii of two circle = 84 cm

=> R+r = 84 ----------(1)

And

The difference of their areas = 5544 cm.

=> πR²-πr² = 5544

=>π(R²-r²) = 5544

=> (22/7)(R²-r²) = 5544

=> R²-r² = 5544×7/22

=> R²-r² = 252×7

=> (R+r)(R-r) = 1764

=> (84)(R-r) = 1764

=> R-r = 1764/84

=> R-r = 21------------(2)

On adding (1)&(2)

R+r = 84

R-r = 21

(+)

__________

2R+0 = 105

__________

=> 2R = 105

=> R = 105/2

=> R = 52.5 cm

On Substituting the value of R in (1)

=> 52.5+r = 84

=> r = 84-52.5

=> r = 31.5 cm

Therefore, R = 52.5 cm and r = 31.5 cm

Answer:-

The radii of the two given circles are 52.5 cm and 31.5 cm respectively.

Used formulae:-

→ Area of the second circle = πr² sq.units

• r = radius
• π = 22/7