Use 3.14 as pi. 100 is the length and 60 is the width.
Alex wants to cut out as many circular badges as possible from this rectangular sheet of cardboard. the diameter of each badge is 14 cm. how many badges can he cut?
First, we need to find the area of the rectangular sheet of cardboard:
Area = length x width
Area = 100cm x 60cm
Area = 6000cm²
Next, we need to find the area of one circular badge:
Radius = diameter ÷ 2 = 14cm ÷ 2 = 7cm
Area = pi x radius²
Area = 3.14 x 7cm²
Area = 153.86cm²
Now we can find the number of badges that can be cut from the rectangular sheet:
Number of badges = Area of rectangular sheet ÷ Area of one badge
Number of badges = 6000cm² ÷ 153.86cm²
Number of badges ≈ 39.03
Since we can't cut a fraction of a badge, Alex will be able to cut 39 badges from this sheet of cardboard.
To find out how many circular badges Alex can cut from the rectangular sheet of cardboard, we need to calculate the area of the rectangular cardboard and the area of each circular badge.
The area of a rectangle can be calculated by multiplying its length and width:
Area of rectangle = length * width
Given:
Length = 100 cm
Width = 60 cm
Area of rectangle = 100 cm * 60 cm
Area of rectangle = 6000 cm^2
The area of a circle can be calculated using the formula:
Area of circle = pi * (radius)^2
Given:
Diameter of each badge = 14 cm
Radius of each badge = Diameter / 2 = 14 cm / 2 = 7 cm
Substituting the values into the formula, the area of each badge is:
Area of badge = 3.14 * (7 cm)^2
Area of badge = 3.14 * 49 cm^2
Area of badge = 153.86 cm^2 (rounded to two decimal places)
Now, we can find the number of badges that can be cut from the rectangular sheet by dividing the area of the rectangle by the area of each badge:
Number of badges = Area of rectangle / Area of badge
Number of badges = 6000 cm^2 / 153.86 cm^2
Using a calculator or rounding manually, we can calculate the number of badges Alex can cut.
Number of badges ≈ 38.99
Since the number of badges cannot be fractional, we need to round down to the nearest whole number as we cannot have partial badges.
Therefore, Alex can cut out a maximum of 38 circular badges from the rectangular sheet of cardboard.