Question

what is the radius of a circle whose area is equal to the sum of the areas of two circles of radii 14 cm and 9 cm






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Answer 1

$\tt{ \underbrace{Concept \: \: of \: \: the \: \: question \: :-}}$

• It is given in the question that area of first circle is equal to the area of other two circles.

→ It means that we have to find the area of 2nd and 3rd circle and then we will add it.

• After adding, the area obtained will be equal to area of 1st circle.

• From this area we will find the radius of 1st circle.

Given :-

◍ Radius of 2nd circle = 14 cm

◍ Radius of 3rd circle = 9 cm

Solution :-

$\mapsto \: \tt{Area \: \: of \: \: 2nd \: \: circle = \pi \times (radius \: \: of \: \: 2nd \: \: circle)^{2} } \\ \\ \mapsto \: \tt{Area \: \: of \: \: 2nd \: \: circle = \dfrac{22}{7} \times (14 \: cm)^{2} }\\ \\ \mapsto \: \tt{Area \: \: of \: \: 2nd \: \: circle = \dfrac{22}{7} \times 196 \: cm^{2} }\\ \\ \mapsto \: \tt{Area \: \: of \: \: 2nd \: \: circle = 22 \times 28\: cm^{2} }\\ \\ \mapsto \: \tt{Area \: \: of \: \: 2nd \: \: circle = 616\: cm^{2} }$

Now, finding the area of 3rd circle.

$\mapsto \: \tt{Area \: \: of \: \: 3rd \: \: circle = \pi \times (radius \: \: of \: \: 3rd \: \: circle)^{2} } \\ \\ \mapsto \: \tt{Area \: \: of \: \: 3rd \: \: circle = \dfrac{22}{7} \times (9 \: cm)^{2} }\\ \\ \mapsto \: \tt{Area \: \: of \: \: 3rd \: \: circle = \dfrac{22}{7} \times 81 \: cm^{2} }\\ \\ \mapsto \: \tt{Area \: \: of \: \: 3rd \: \: circle = \dfrac{1782}{7} \: cm^{2} }\\ \\ \mapsto \: \tt{Area \: \: of \: \: 3rd \: \: circle = 254.5\: cm^{2} }$

$➝ \tt{Area \: \: of \: \: 1st \: \: circle = Area \: \: of \: \: 2nd \: \: circle \: + \: Area \: \: of \: \: 3rd \: \: circle} \\ \\ ➝ \tt{Area \: \: of \: \: 1st \: \: circle = 616 \: cm^{2} +254.5\: cm^{2} } \\ \\ ➝ \tt{Area \: \: of \: \: 1st \: \: circle = 870.5\: cm^{2} }$

Now, we have area of 1st circle with the help of this we will find the radius of 1st circle.

$\mapsto \: \tt{Area \: \: of \: \: 1st \: \: circle = \pi \times (radius \: \: of \: \: 1st \: \: circle)^{2} } \\ \\ \mapsto \: \tt{870.5 \: {cm}^{2} = \dfrac{22}{7} \times (radius \: \: of \: \: 1st \: \: circle)^{2} }\\ \\ \mapsto \: \tt{ \dfrac{870.5 \times 7}{22} \: {cm}^{2} =(radius \: \: of \: \: 1st \: \: circle)^{2} }\\ \\ \mapsto \: \tt{276.9\: {cm}^{2} = (radius \: \: of \: \: 1st \: \: circle)^{2}}\\ \\ \mapsto \: \tt{ \sqrt{276.9 \: {cm}^{2}}= radius \: \: of \: \: 1st \: \: circle}\\ \\ \mapsto \: \tt{16.6 \: cm= radius \: \: of \: \: 1st \: \: circle}$

Therefore, radius of 1st circle = 16.6 cm

More Information :-

✧ Circumference of the circle = π × diameter

Diameter = 2 × radius

So,

Circumference of the circle= 2 × π × radius

✧ Perimeter of square = 4 × side of square

✧ Area of square = (side of square)²

✧ Perimeter of the rectangle = 2(Length + Breadth)

✧ Area of the rectangle = Length × Breadth