Hello, alibond07!

You need to know the area of a circle and some common sense.

Exactly where is your difficulty?

A circular dartboard is divided into 20 equal sectors,

one of which is shown in the diagram. O is the centre of the circle.

The areas for scoring double and treble are marked A and B respectively.

Find the ratio (area A) : (area B) in the form n : 1, giving n correct to 1 d.p

OM: 99mm . MN: 8mm . OP: 162mm . PQ: 8mm This is a diagram of the radii: Code:

: - - - - 107 - - - :
: - - -99 - - :
(A) (B)
O ----------- M --- N ------- P --- Q
: - - - - - - - 162 - - - - - :
: - - - - - - - - 170 - - - - - - - :

The circle with radius $\displaystyle OQ = 170$ has area: .$\displaystyle \pi(170^2)$

The circle with radius $\displaystyle OP = 162$ has area: .$\displaystyle \pi(162^2)$

. . The area of ring $\displaystyle A$ is: .$\displaystyle 28,\!900\pi - 26,\!244\pi \:=\:2656\pi$

The circle with radius $\displaystyle ON = 107$ has area: .$\displaystyle \pi(107^2)$

The circle with radius $\displaystyle OM = 99$ has area: .$\displaystyle \pi(99^2)$

. . The area of ring $\displaystyle B$ is: .$\displaystyle 11,\!449\pi - 9801\pi \:=\:1648\pi $

Hence: .$\displaystyle \frac{\text{ring A}}{\text{ring B}} \:=\:\frac{2656\pi}{1648\pi} \;=\;1.611650485$

Therefore: .$\displaystyle \text{(area A)} : \text{(area B)} \;\approx\;1.6:1$