Question

If the sum of the areas of two circles with radii 3cm and 4cm is equal to the area of a circle of

radius R, then find the value of R.​

Answer 1

R=5cm

Step-by-step explanation:

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Answer 2

Given: If the sum of the areas of two circles with radii 3cm and 4cm is equal to the area of a circle of  radius R.

To find: the value of R.

Solution:

Form the equation according to the condition given in the question, to find the value of R.

$\[\begin{array}{l}\pi {R^2} = \pi \times {3^2} + \pi \times {4^2}\\ \Rightarrow \pi {R^2} = \pi \left( {{3^2} + {4^2}} \right)\\ \Rightarrow {R^2} = \left( {{3^2} + {4^2}} \right)\\ \Rightarrow {R^2} = \left( {9 + 16} \right)\end{array}\]$

$\[\begin{array}{l} \Rightarrow {R^2} = 25\\ \Rightarrow {R^2} = 5cm\end{array}\]$

Hence, the value of R is 5 cm.