GATE CS 2020 Set 1 — Question 8
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General Aptitude → Quantitative Aptitude → Mensuration & Geometry
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Question
The figure below shows an annular ring with outer and inner radii as and , respectively. The annular space has been painted in the form of blue colour circles touching the outer and inner periphery of annular space. If maximum number of circles can be painted, then the unpainted area available in annular space is ______.
Correct answer
(A) π [(b² - a²) - (n)/(4)(b-a)²]
Solution
1.Area of the Annular Ring:
The outer radius is and the inner radius is .Area of annulus = Area of outer circle - Area of inner circle
2.Area of Small Circles:
The small circles touch both the inner and outer periphery. Thus, their diameter is the difference between the outer and inner radii.Diameter
Radius
Area of one small circle =
3.Total Painted Area:
There are such circles.Total area of circles =
4.Unpainted Area:
Unpainted Area = Area of Annulus - Total Area of CirclesThis matches option (A).
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