Question

find the diameter of a circle whose area is equal to the sum of the areas of the two circles of radius 40 cm and 9 CM

Answer 1

Let the radius of circle is r, whose area is equal to the sum of the areas of the two circles of radius 40 cm and 9 CM

Area of circle having radius 40=
$\pi( {40)}^{2}$
Area of circle having radius 9=
$\pi( {9)}^{2}$
Area of circle radius r
$= \pi {r}^{2}$
A.T.Q

$\pi( {r)}^{2} = \pi( {40)}^{2} + \pi( {9})^{2} \\ \\ {r}^{2} = 1600 + 81 \\ \\ {r}^{2} = 1681 \\ \\ r = 41 cm$
Diameter= 2r

=2×41

= 82 cm