A circular dartboard has a diameter of 84 cm and is divided into four concentric scoring zones from the centre outward: gold, silver, bronze, and black. The gold zone has a radius of 14 cm, while the other three zones have equal widths. If a dart lands randomly on the board, what is the probability that it lands in the gold zone?

(a) 1/8

(b) 1/4

(c) 1/9

(d) 1/10

Question

A circular dartboard has a diameter of 84 cm and is divided into four concentric scoring zones from the centre outward: gold, silver, bronze, and black. The gold zone has a radius of 14 cm, while the other three zones have equal widths. If a dart lands randomly on the board, what is the probability that it lands in the gold zone?

(a) 1/8

(b) 1/4

(c) 1/9

(d) 1/10

ONLiNE UPSC · Accepted Answer

Total radius = 42 cm (since diameter = 84 cm)

Gold zone radius = 14 cm

Remaining width = 42 &ndash; 14 = 28 cm 

Probability that dart lands in gold zone:

Area of gold/Area of board = (&pi; * 142) / (&pi; * 422) = 196/1764 = 1/9

Hence, correct option is c.

Geometry

Circle - Probability

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