Geometric Probability: Area Ratios in Shapes Quiz

A dartboard is circular with a radius of 10 cm. If a dart is thrown randomly at the board, what is the probability that it lands within a smaller circle of radius 5 cm?

• 0.1

• 0.25

• 0.5

• 0.75

A rectangular garden measures 20 m by 10 m. If a random point is chosen within the garden, what is the probability that the point lies within a flower bed that occupies a rectangle of 4 m by 2 m?

• 0.5

• 0.2

• 0.04

• 0.1

A circular swimming pool has a radius of 8 m. If a person randomly swims in the pool, what is the probability that they are within 3 m of the edge of the pool?

• 15/32

• 25/64

• 39/64

• 1/2

A square park has a side length of 50 m. If a random point is selected within the park, what is the probability that the point is within a circular fountain with a radius of 5 m located at the center of the park?

• 0.0314

• 0.005

• 0.1

• 0.0628

A triangular plot of land has vertices at (0,0), (6,0), and (3,5). If a point is chosen randomly within this triangle, what is the probability that the point lies within a smaller triangle formed by the vertices (1,1), (2,1), and (1.5,3)?

• 1/10

• 1/5

• 1/20

• 1/15

Tags

CCSS.6.G.A.3

A rectangular field is 100 m long and 50 m wide. If a random point is selected in the field, what is the probability that it lies within a 10 m by 10 m square located at one corner of the field?

• 0.1

• 0.02

• 0.1

• 0.05

A circular pizza has a diameter of 12 inches. If a slice is cut out that has a central angle of 60 degrees, what is the probability that a randomly chosen point on the pizza is within the slice?

• 1/6

• 1/2

• 1/3

• 1/4

Tags

CCSS.4.MD.C.5B

CCSS.HSG.CO.A.1

A rectangular swimming area is 30 m by 15 m. If a random point is chosen in the area, what is the probability that it lies within a circular area of radius 3 m located at the center of the swimming area?

• 0.0314

• 0.1570

• 0.1256

• 0.0628

A square playground has a side length of 40 m. If a random point is chosen within the playground, what is the probability that it lies within a circular sandbox with a radius of 4 m located at one corner of the playground?

• 0.0314

• 0.0157

• 0.0628

• 0.1256

A circular track has a radius of 20 m. If a runner randomly selects a point on the track, what is the probability that the point is within 2 m of the inner edge of the track?

• 0.81

• 0.25

• 0.50

• 0.65