Question

6. The radii of two circles are 4cm and 3 cm respectively. The diameter of the cicla
having area equal to the sum of the area of two circle is
(a) 5cm (b)7cm (c) 10cm (d) 14cm​

Answer 1

Answer:

Given :

The radii of two circles are 4cm and 3cm respectively .

To Find :

The diameter of the circle having area equal to the sum of the area of the two circles .

Solution :

___________________________

Area of the circle having radius 3cm

→ Area = πr²

→ 3.14 × 3²

→ 3.14 × 9

→ 28.26 cm²

Area of circle having radius 3cm is 28.26 cm²

___________________________

Area of the circle having radius 4cm

→ Area = πr²

→ 3.14 × 4²

→ 3.14 × 16

→ 50.24 cm²

Area of circle having radius 3cm is 50.24 cm²

___________________________

Sum of the areas of the two circles

→ 28.26 cm² + 50.24 cm²

→ 78.50 cm²

___________________________

Now, we have to find the diameter of the circle having area 78.50 cm²

→ Area of circle = πr²

→ 78.50 = 3.14 × r²

→ r² = 78.50/3.14

→ r² = 25

→ r = 5 cm

___________________________

Diameter = 2 × radius

→ d = 2 × 5

→ d = 10 cm

So, the diameter of the circle having area 78.50 cm² is 10 cm .