Find the Diameter of the Circle Whose Area is Equal to the Sum of the Areas of Two Circles Having Radii 4 Cm and 3 Cm. - Mathematics

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Sum

Find the diameter of the circle whose area is equal to the sum of the areas of two circles having radii 4 cm and 3 cm.

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Solution

Let the diameter of the required circle be d.

Now, of the required circle = Are of circle having 4 cm + Area of circle having radius 3 cm

`⇒pi("d"/2)^2=pi(4)^2+pi(3)^2`

`=>("d"/2)^2 = 16 + 9`

`=>("d"/2)^2 = 25 =(5)^2`

`=>"d"/2 = 5`

⇒ d = 10 cm

Hence, the diameter of the circle is 10 cm.

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Chapter 18: Area of Circle, Sector and Segment - Exercise 18A [Page 819]

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RS Aggarwal Secondary School Class 10 Maths
Chapter 18 Area of Circle, Sector and Segment
Exercise 18A | Q 7 | Page 819

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