Question

find the diameter of the circle whose area is equal to the sum of the areas of the two circles of diameter 20 cm and 48 centimetres​

Answer 1

Answer:

$\large\bold\red{52\:\:cm}$

Step-by-step explanation:

Let the radius of the required circle be r.

Now,

Given,

A circle having diameter = 20 cm

Therefore,

Radius = 10 cm

Therefore,

It's area is given by,

$= \pi {(10)}^{2} \\ \\ = 100\pi \: \: {cm}^{2}$

Now,

Another circle is having diameter = 48 cm

Therefore,

Radius = 24 cm

Therefore,

It's area is given by,

$= \pi {(24)}^{2} \\ \\ = 576\pi \: \: {cm}^{2}$

But,

It's given that,

The sum of these both areas of circles is equal to the area of the required circle .

Therefore,

We get,

$= > \pi {r}^{2} =100\pi + 576\pi \\ \\ = > \pi {r}^{2} = 676\pi \\ \\ = > {r}^{2} = 676 \\ \\ = > {r}^{2} = {(26)}^{2} \\ \\ = > r = 26 \: \: cm$

Therefore,

Radius of required cirlce = 26 cm

Hence,

Diameter = 52 cm

Answer 2

Answer:

Diameter of the circle is 52 cm

$\rule{100}2$

Step-by-step explanation:

Given:-

• The diameter of one circle = d' = 20 cm
• R' = d'/2 = 10 cm
• The diameter of another circle = d" = 48 cm
• R" = d"/2 = 24 cm

Find:-

Diameter of the circle whose area is equal to the sum of area of two circles.

Solution:-

We know that -

Area of circle = πr²

According to question,

Sum of areas of two circle is equal to area of circle.

πr² = π(r')² + π(r")²

Substitute the known values in above formula

⇒ πr² = π(10)² + π(24)²

⇒ r² = 100 + 576

⇒ r² = 676

⇒ r = √676

⇒ r = 26 cm

So, diameter of circle = 2r

⇒ 2(26)

⇒ 52 cm

$\rule{200}2$