In the diagram, the width of the rectangle is 8.0 units, the height of the rectangle is 6.5 units, and the radius of the circle is 3.0 units. If 1000 darts are thrown at the rectangle, approximately how many darts would you expect to land in the circle?

Question

Mikaela Patel

Mathematics

4 September, 04:03

In the diagram, the width of the rectangle is 8.0 units, the height of the rectangle is 6.5 units, and the radius of the circle is 3.0 units. If 1000 darts are thrown at the rectangle, approximately how many darts would you expect to land in the circle?

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Jesus · Answer 1

The probability of hitting inside the circle, assuming that you at least hit the rectangle, is the area of the circle divided by the area of the entire rectangle.

P (C) = (πr^2) / (xy)

P (C) = (π3^2) / (8*6.5)

P (C) = 9π/52

So you would expect to land in the circle 1000 (P (C)):

9000π/52 which is approximately:

543.73 times