Find the area of bull eye and each ring of target

Question

Jaylen Fountain · Accepted Answer

how to find:

Accepted Answer

a) Given: radius = 1,2,3,4

Area of circles with radius 1,2

$A_{1} = π r_{1}^{2}$

$A_{1} = π (1)^{2} = π$

$A_{2} = π (2)^{2} = 4 π$

Now the area ofthe first ring is the difference of area of second circle and bull eye. Thus:

$A = 4 π - π$

$A = 3 π$

i.e. the area ofthe first ring is $3 π$ . Now area of circles with radius 3,4.

$A_{1} = π r_{1}^{2}$

$A_{3} = π (3)^{2} = 9 π$

the area of the second ring is the difference of area of circle with radius three and two.

$A = 9 π - 4 π = 5 π$ Area of circle with radius 4

$A = π r_{1}^{2}$

$A_{4} = π (4)^{2} = 16 π$

Area of third ring. $A = 16 π - 9 π = 7 π$

Hence, the area of the rings are $3 π, 5 π, 7 π$

b) Area of circle with radius (n+1) is

$A = π (n + 1)^{2}$

Area of circle with radius n is

$A = π (n)^{2}$

Now area of nth ring is

$A = π (n + 1)^{2} - π n^{2}$

$A = (2 n + 1) π$

Answered question