Question

Find the diameter of a circle whose circumference is equal to the sum of circumferences of circles with radii 10 cm , 12cm , 18cm

Answer 1

Answer:

Step-by-step explanation:

Given :-

Radii of the circumferences = 10 + 12 + 18 = 40 cm

To Find :-

Diameter of a circle

Solution :-

Let the radius of the circle = R cm

2πR = 2π × 10 + 2π × 12 + 2π × 18

On dividing each term by 2π, we get:

R = 10 + 12 + 18 = 40 cm

Radius of the circle obtained = 40 cm

And, its diameter = 2 × Radius

Diameter  = 2 × 40 cm = 80 cm

Hence, the Diameter of a circle is 80 cm.

Answer 2

Solution :

Given:

Radii of the circumferences:

$\implies$ 10 + 12 + 18

$\implies$ 22 + 18

$\implies$ 40 cm

Let the radius of the circle be 'R' cm.

We have to find: Diameter of a circle

Now:

Sum of circumferences (3 circles),

$\implies$ $\boxed{\sf{2 \pi R = 2 \pi \times 10 + 2 \pi \times 12 + 2 \pi \times 18}}$

So,

Dividing each term by 2π, we get:

$\implies$ $\frac{2\pi R}{2\pi} = \frac{2\pi \times 10}{2\pi} + \frac{2\pi \times 12}{2\pi} + \frac{2\pi \times 18}{2\pi}$

$\implies$ R = 10 + 12 + 18

$\implies$ R = 22 + 18

$\implies$ R = 40 cm

Hence,

Radius of the circle obtained is 40 cm.

And,

$\implies$ Diameter = 2 × Radius

$\implies$ Diameter = 2 × 40

$\implies$ Diameter = 80 cm

Therefore:

The diameter of a circle whose circumference is equal to the sum of circumferences of circles with radii 10 cm, 12 cm and 18 cm is 80 cm.