The width of the circular ring is equal to the radius of the inner circle of the ring if the radii of the inner and outer circle are r and R then the area of the circle ring is:

Subject; Mathematics

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2 {πR}^{2}

2 {πr}^{2}

3 π R^{2}

3 π r^{2}

answer is D.

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Detailed Solution

Concept- We will use the standard formula for the area of a ring which is

A = π (R^{2} - r^{2})

The width of the circular ring is equal to the inner radius r,
So, the outer radius becomes

R = r + r = 2 r

Area of the region between two concentric circles with radius of outer circle R, and the inner circle r,

A = π (R^{2} - r^{2})

Hence, the area of the given ring

= π (R^{2} - r^{2})

Put R = 2r in equation(i), we get

A = π (2 r) 2 − r 2

A = 4 π r 2 − π r 2

A = 3 π r 2

Therefore, the area of the given circular ring

= 3 π r^{2}

Hence, the correct answer is option 4.

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