Question

The radii of two circles are 8cm and 6cm. Find the radius of the circle having its
area equal to the sum of the area of the two circles. ​

Answer 1

Answer:-

Given:

Radii of two circles are 8 cm , 6 cm.

Also,

Sum Areas of two circles = Area of the other circle.

We know that

Area of a circle = πr²

where r is the radius.

Let the radius of the other circle be r.

According to the question,

⟶ π(8)² + π(6)² = πr²

⟶ π(64 + 36) = π(r²)

⟶ 100 = r²

⟶ √100 = r

⟶ ± 10 = r

radius of a circle cannot be negative. So , positive value is taken.

∴ The radius of the other circle is 10 cm.

Answer 2

Answer:

$\huge \bf \: answer$

As we are knowing that radii of two circle are 8cm and 6cm.

Sum area of two circle = area of other circle

$\huge \bf \: area \: = \pi {r}^{2}$

$\sf \: \pi {(8)}^{2} + \pi {(6)}^{2} = \pi {r}^{2}$

$\pi(64 + 36) = \pi {r}^{2}$

$\sf \: 100 = {r}^{2}$

$\sf \sqrt{100} = r$

$\sf \: r \: = 10$

Radius = ± 10

Radius can't be taken as negative.

$\huge \bf \therefore \: r \: = 10 \: cm$

Here

R - Radius.

π = 3.14 or 22/7