# the radius of the ring

An archer is to fire arrows at a target of concentric circles. The target - maker wishes to calculate the cross - sectional areas of the rings A, B, C and D of the target to make their areas in the ration of 4:3:2:1. The whole target is of radius 10 cm.

(i) Calculate the fraction of the total area of the target filled by each of the regions A, B, C, D

(ii) Find an expression for the area of the target, leaving your answer as a multiple of =/

(iii) Find an expression for each area A, B, C, D leaving your answer as a multiple of =/

(iv) Show that the inner radius of ring A is squared root 60cm, and find similar expressions for the inner radii of ring B and ring C. (Leave your answers as square roots).

Please show your work.

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#### Solution Summary

This posting finds the radius of the ring.