Use 3.14 as pi.
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 each circular badge using the given diameter:
Radius = diameter/2 = 14/2 = 7 cm
Area of a circle = pi x radius^2
Area of a badge = 3.14 x 7^2 = 153.86 cm^2
Next, we need to find the total area of the rectangular cardboard sheet:
Length = ?
Width = ?
Area of rectangle = Length x Width
Unfortunately, we don't have enough information to find the length and width of the cardboard sheet. We can't solve the problem with the given information.
To determine how many badges Alex can cut from the rectangular sheet of cardboard, we need to calculate the maximum number of circles that can fit in the rectangle.
The diameter of each badge is 14 cm, which means the radius of each badge is half of the diameter, i.e., 14 cm / 2 = 7 cm.
Now, we need to find the dimensions of the rectangle:
Since the diameter of each badge is 14 cm, the width of the rectangle should be a multiple of 14 cm. Let's say the width is W cm.
The length of the rectangle should also be a multiple of 14 cm. Let's say the length is L cm.
Now, we can calculate the maximum number of badges that can be cut from the rectangle:
The width of the rectangle can fit the maximum number of badges: W / (2 * radius) = W / (2 * 7) = W / 14
The length of the rectangle can fit the maximum number of badges: L / (2 * radius) = L / (2 * 7) = L / 14
Thus, the maximum number of badges that can be cut is the product of the width and length of the rectangle, divided by the area of each badge (π * radius^2):
Number of badges = (W / 14) * (L / 14) = (W * L) / 196
Please provide the width and length of the rectangular sheet of cardboard so that the calculation can be completed.