Question

4) The radii of two circles are 4 cm and 3cm Find the diameter
of a circle having area equal to the sum of the areas
of two circles,​

Answer 1

Given

$\sf{ \to R_2= 4cm} \\ \\ \sf{ \to R_3 = 3 cm}$

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Concept used

Here the concept of circle and its area is used. Radius of two circles is given as 4 cm and 3 cm. we will simply add the area of given circle and equate it with the area of new circle. From there we will find the radius of new circle. Then find the diameter of new circle

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Formula used

$\bull \bold{ \red{Area \: of \: circle= πr²}}$

$\bold{\bull \:\pink{diametre = 2r}}$

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Solution

$\sf{ \orange{Let \: us \: Assume \: the \: radius \: of \: unknôwn \: circle as \: R_1 }}$

So,

»Sum of the area of given circle will be given as

$\sf{\implies πR²_2+πR²_3}\\ \\ \sf{\implies π(R²_2+R²_3)}$

$\sf{\implies π (4²+3²)} \\ \\ \sf{\implies π (16+9)}$

${\implies \green{ 25π \: cm ^{2} }. } \: \: \: \: \: \: ..(i)$

»Now area of new circle

${\implies \red{ πR²_1 \: {cm}^{2} }} \: \: \: \: ..(ii)$

»Equate equation (i) and (ii)

$\bold{{\implies \purple{ πR²_1= 25π}}}$

»π get cancelled

$\sf{\implies R²_1= 25} \\ \\ \sf{\implies \blue{ R_1 = 5 cm}}$

Therefore the radius of new circle is 5cm

$\bold{Diameter = 2r }\\ \\ \sf{ \implies Diameter= 2× 5 }\\ \\ \sf{ \implies \green{Diameter= 10 cm}}$

➢Therefore the Diameter of new circle is 10 cm

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