Question

(1)

The diameters of the three circles are in the ratio 3 : 5 : 6. If the sum of the circumferences of these circles be 308cm; find the difference between the areas of the largest and the smallest of these circles.

(2)

Two circles touch each other externally. The sum of their areas is 74π cm² and the distance between their centres is 12 cm. Find the diameters of the circles.​

Answer 1

(1) Given,

Diameter of three circle=3:5:6

Sum of the circumference=308cm

Let the diameter of the circles be 3x,5x,6x

Now,

 π(3x)+π(5x)+π(6x)=308

=14xπ=308

=x=  308/2 x 22

=x=7

Therefore,

Diameter of the largest side=6 x 7 =42

Radius of largest circle=  6 x 7/2  =21

Diameter of the smallest circle=3x

                                               =3×7   =21

                                             

Radius of smallest circle=  3 x 7/2    =10.5

Difference of areas of largest and smallest of the circles=

π(21)  2 −(π(10.5)  2  =   =1039.5cm  2

(2) Let the radius of the circles be r1

and r2,

So, r +2 = 12 =

r2 = 12-r1

Sum of the areas of the circles =74π

=>πr1²+ πR1²= 74π

=>r12+r2²= 74

=> I2+ (12- r1)² = 74

=>r1²+144-24r1 + r1² = 74

=>2r1²-24r1 +70=0

=>r1²-12r1+35 = 0

=>(r1-7)(r1-5) = 0

=> (r1-7)(r1-5)=0

=> r1=7 or r1 =5

Ir r1= 7 cm, then r2=5 cm

If r1=5 cm, then r2 = 7 cm

So, the diameters of the circles will

10 cm and 14 cm.

Hope it helps you ✌

 

                                                                             

Answer 2

iven,

Diameter of three circle=3:5:6

Sum of the circumference=308cm

Let the diameter of the circles be 3x,5x,6x

Now,

 π(3x)+π(5x)+π(6x)=308

=>14xπ=308

=>x=  

2×22

308

​  

 

=>x=7

Therefore,

Diameter of the largest side=6×7

                                           =42

Radius of largest circle=  

2

6×7

​  

 

                                   =21

Diameter of the smallest circle=3x

                                               =3×7

                                               =21

Radius of smallest circle=  

2

3×7

​  

 

                                     =10.5

Difference of areas of largest and smallest of the circles=π(21)  

2

−(π(10.5)  

2

 

                                                                               =1039.5cm  

2