Question

The radii of two circles are 4 cm and 20 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles..

#Answer. *​

Answer 1

$\huge \color{red} ☆ANSWER☆$

$let \: r1 = 4cm \: and \: r2 = 3cm$

$Now, area \: of \: new \: circle =πr \frac{1}{2} +πr \frac{2}{2}$

$\pi {r}^{2} = \frac{22}{7} ( ({4})^{2} + {(3)}^{2} )$

$\frac{22}{7} \times {r}^{2} = \frac{22}{7} \times 25$

${r}^{2} = 25$

$r = 5cm$

$∴Diameter \: of \: new \: circle =2r=10cm.$

Answer 2

Answer:

letr1=4cmandr2=3cm

Now, area \: of \: new \: circle =πr \frac{1}{2} +πr \frac{2}{2}Now,areaofnewcircle=πr

2

1

+πr

2

2

\pi {r}^{2} = \frac{22}{7} ( ({4})^{2} + {(3)}^{2} )πr

2

=

7

22

((4)

2

+(3)

2

)

\frac{22}{7} \times {r}^{2} = \frac{22}{7} \times 25

7

22

×r

2

=

7

22

×25

{r}^{2} = 25r

2

=25

r = 5cmr=5cm

∴Diameter \: of \: new \: circle =2r=10cm.∴Diameterofnewcircle=2r=10cm.