Question

C. Find the diameter of the circle whose circumference is equal to the sum of the
circumferences of the circles with radii 8cm, 10cm and 12 cm respectively.​

Answer 1

Answer:

Total Radius= 8+10+12=30cm

Circumference=2πr

C= 2×3.14×30

C=188.4

Therefore as we know,

Circumference=π×Diameter

188.4=3.14×d

d=188.4/3.14= 60cm Answer

Or

As we know

Diameter=2×Radius

d=2×30

d=60cm Answer

Hope this is helpful

Answer 2

Before, finding the answer. Let's find out how we can find the answer.

• First, we have to find the Circumference of all the circles. To find the Circumference of Circle, we must use the formula of :

$\boxed{\sf Circumference \: of \: Circle = 2 \pi r}$

• After, finding the Circumference of all the circles. We must add them all to find the Diameter.

____________________

Given :

• Radius = 8 cm, 10 cm and 12 cm

To find :

• diameter of the circle

Solution :

⇒ Circumference of Circle with radius as 8 cm :

Circumference of Circle = 2πr

                                         = $\sf 2 \times \dfrac{22}{7} \times 8$

                                         = $\sf 16 \times \dfrac{22}{7}$

                                         = $\sf \dfrac{352}{7}$

                                         = 50.28 cm

⇒ Circumference of Circle with radius as 10 cm :

Circumference of Circle = 2πr

                                        = $\sf 2 \times \dfrac{22}{7} \times 10$

                                        = $\sf 20 \times \dfrac{22}{7}$

                                        = $\sf \dfrac{440}{7}$

                                        = 62.85 cm

⇒ Circumference of Circle with radius as 12 cm :

Circumference of Circle = 2πr  

                                        = $\sf 2 \times \dfrac{22}{7} \times 12$

                                        = $\sf 24 \times \dfrac{22}{7}$

                                        $\sf = \dfrac{528}{7}$

                                        = 75.42 cm

Diameter = 50.28 + 62.85 + 75.42

               = 188.55 cm

Therefore, Diameter of the cirlce is 188.55 cm.