Question

Two concentric circles form a target. The radii of the two circles measure 8 cm and 4 cm. The inner circle is the bullseye of the target. A point on the target is randomly selected.

What is the probability that the randomly selected point is in the bullseye?

Enter your answer as a simplified fraction in the boxes.

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Answer 1

Explanation:

The area of the bullseye is the difference between the areas of the two circles:

Area of inner circle = π(4 cm)² = 16π cm²

Area of outer circle = π(8 cm)² = 64π cm²

Area of bullseye = Area of outer circle - Area of inner circle = 64π cm² - 16π cm² = 48π cm²

The total area of the target is the area of the outer circle:

Total area of target = π(8 cm)² = 64π cm²

So the probability of randomly selecting a point in the bullseye is:

Probability = (Area of bullseye) / (Total area of target)

Probability = (48π cm²) / (64π cm²)

Probability = 3/4

Therefore, the probability that the randomly selected point is in the bullseye is 3/4.