You throw a dart at the board shown. Your dart is equally likely to hit any point inside the square board
1 answer:
This question is incomplete and the picture of the board is not attached.
Find attached to this answer the picture of the board.
Complete question
You throw a dart at the board shown. Your dart is equally likely to hit any point inside the square. What is the probability your dart lands in the yellow region?
Answer:
56.32%
Step-by-step explanation:
From the attached diagram, we can see different sections on the board, with different colours as well.
We have the
a. Blue square shape
b. Yellow region circular shape
c. Green region triangular shape
White region = square shape
Red region = circular shape
Step 1
We need to determine the area of the
various shapes.
First, we find the areas of all the shapes in the dartboard.
The Blue Square shape and the Area of a square = Length of the sides ²
Length of the side = 18 inches
The area of the square = 18²= 324 square inches.
The yellow circular in shape
Area of a circle = πr²
Since the circle is found in a square, the diameter of the circle = Length of the square side
So, diameter of the circle = 18 inches.
Radius of a circle = Diameter ÷ 2
Radius of the circle = 18 inches ÷ 2 = 9 inches.
The area of a circle = π × 9² = 254.469 square inches.
The Green triangular shape
We have 2 green triangles and looking at the attached diagram, the base of both = 6 inches and a height of 6 inches as well.
Area of a triangle = 1/2 × base × height
Area of a triangle = 1/2 × 6inches × 6 inches.
= 18 square inches.
For the two triangles , their combined areas = 2 × 18 square inches = 36 square inches.
We have a small inner square painted white with a side length of 6 inches.
Area of the square = s² = (6² inches) = 36 inches² = 36 square inches.
We also have a small inner circle as well which is coloured red
Area of a circle = πr²
Since the circle is found in a square, the diameter of the circle = Length of the square side
So, diameter of the circle = 6 inches.
Radius of a circle = Diameter ÷ 2
Radius of the circle = 6 inches ÷ 2 = 3 inches.
The area of a circle = π × 3² = 28.274 square inches.
Since, the area of the entire board is the same as the outer square area.
The area of the blue region = Area of the outer square - Area of the outer circle = 324 - 254.469 = 69.531 square inches.
The area of the yellow region =
Area of the outer circle - Area of 2 triangles - Area of the inner square
Area of the outer circle = 254.469 square inches
Area of 2 triangles = 36 square inches
Area of the inner square = 36 square inches
= (254.469 - 36 - 36) square inches. = 182.469 square inches.
The final step would be to find the probability.
Formula for probability =
number of favorable outcomes ÷ the total number of outcomes.
The probability of dart landing on yellow region =
182.469 square inches ÷ 324 = 0.5631759259
= 56.32%
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