Question

The radius of circles are 8 cm and 6 cm .find the radius of the two circles having are equalto the sum of the areas

Answer 1

We have to find the radius of the circle, which has the area equal to the sum of these two circle's area.


Area of a circle = πr²

For first circle, r = 8 cm

=> area = π8²

=> area = 64π cm²


R of second circle = 6 cm

=> area = π6²

=> area = 36π cm²


Now we have to add them

64π + 36π = 100π

We have to find the radius of the circle whose area is 100π cm²

Let the radius be R

So area = πR²

=> πR² = 100π

=> R² = 100π/π

=> R² = 100

=> R = √100

=> R = 10 cm


Your answer :- 10 cm

Answer 2

According to question we have given;

$\textbf{radius of circles = 8 cm and 6 cm}$

$\textbf{Let radius of one circle be 8 cm}$

And

$\textbf{Radius of another circle be 6 cm}$

means;

$r1 \: = \: 8 \: cm$

and

$r2 \: = \: 6 \: cm$

So, Area of circle = πr²

A1 (Area of one circle) = π (8)²

= 64 π cm

A2 (Area of another circle) = π (6)²

= 36 π cm

Now,

We have to find the

$\textbf{Area of a actual circle}$

i.e.

$\textbf{Area of actual circle}$ = $\textbf{Area of one circle + Area of another circle.}$

[According to question]

$\textbf{Area of actual circle}$ = π R²

Means,

π R² = 64 π + 36 π

π R² = 100 π

π cancel on both side....

R² = 100

R = √100

R = 10 cm

ANSWER...

$\huge\textbf{10 cm}$

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