Question

What is the diameter of a circle whose area is equal to the sum of the area of the two circle radii 40 cm and 9 cm

Answer 1

Radius = 41 cm

Diameter = 82 cm

Answer 2

GiveN:

• Area is equal to the sum of the area of the two circle radii 40 cm and 9 cm

To FinD :

• Diameter of the circle

SolutioN:

• Let r be the radius if the circle

$\color {blue} \star \: { \pink{ \boxed{ \bf Area \: of \: circle = \pi {r}^{2} }}} \: \color {blue} \star</p><p>$

According to Question :

$\underline{ \bf{\pi {r}^{2} = \pi \times {40}^{2} + \pi \times {9}^{2}}} \\ \\ : \implies \sf {r}^{2} = 1600 + 81 \\ \\ \\ : \implies \sf {r}^{2} = 1681 \\ \\ \\ : \implies\sf \: r = \sqrt{1681} \\ \\ {\pink{\sf{ :\implies{ \underline {r = 41 \: cm}}}}} \: \color{blue}\bigstar$

${\underline{ \bf { Diameter = 2r }}} \\ \\ : \implies \sf \: 2 × 41 \\ \\ : \red{ \implies \sf \: 82 cm} \: \color {blue} {\bigstar }$

Hence,

• Diameter of circle is 82 cm