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. He can cut 39 badges out of the sheet of paper so what is the area of the carboard left over?
First, we need to determine the area of each circular badge. We know that the diameter is 14 cm, so the radius is half of that, or 7 cm.
Using the formula for the area of a circle, A = pi*r^2, we can calculate the area of each badge:
A = 3.14 * 7^2
A = 153.86 cm^2
Next, we need to determine how many badges we can cut out of the rectangular sheet of cardboard. We know that the length is 100 cm and the width is 60 cm. We can fit the badges in rows and columns, so we need to divide the length and width by the diameter of each badge:
100 cm / 14 cm ≈ 7.14 (round down to 7)
60 cm / 14 cm ≈ 4.29 (round down to 4)
We can fit 7 badges in a row and 4 rows in the width, giving us a total of 28 badges. However, since Alex can cut out 39 badges, we know that he must have some leftover space.
To determine the area of the cardboard leftover, we need to subtract the total area of the badges from the area of the rectangular cardboard:
Total area of badges = 39 badges * 153.86 cm^2/badge
Total area of badges = 5994.54 cm^2
Area of cardboard = length * width
Area of cardboard = 100 cm * 60 cm
Area of cardboard = 6000 cm^2
Area of cardboard leftover = Area of cardboard - Total area of badges
Area of cardboard leftover = 6000 cm^2 - 5994.54 cm^2
Area of cardboard leftover = 5.46 cm^2
Therefore, Alex has 5.46 cm^2 of cardboard leftover.
To find the area of the cardboard left over, we need to first calculate the total area occupied by the circular badges, and then subtract it from the total area of the cardboard.
Step 1: Find the area occupied by each circular badge.
The diameter of each badge is given as 14 cm, so the radius can be calculated as half of the diameter, which is 7 cm.
Using π = 3.14, we can calculate the area of each badge using the formula: Area = π * radius^2.
Area of each badge = 3.14 * (7 cm)^2.
Step 2: Find the total area occupied by all the badges.
As there are 39 badges, the total area occupied by all the badges can be calculated as: Total area = Area of each badge * Number of badges.
Total area occupied by all the badges = 3.14 * (7 cm)^2 * 39.
Step 3: Find the area of the cardboard left over.
The length of the cardboard is given as 100 cm and the width as 60 cm.
The total area of the cardboard can be calculated as: Total area of cardboard = Length * Width = 100 cm * 60 cm.
Now, we can find the area of the cardboard left over by subtracting the total area of all the badges from the total area of the cardboard:
Area of cardboard left over = Total area of cardboard - Total area occupied by all the badges.
Area of cardboard left over = (100 cm * 60 cm) - (3.14 * (7 cm)^2 * 39).
Calculating the values:
Area of each badge = 3.14 * (7 cm)^2 = 3.14 * 49 cm^2 ≈ 153.86 cm^2.
Total area occupied by all the badges = 3.14 * (7 cm)^2 * 39 ≈ 5998.86 cm^2.
Area of cardboard left over = (100 cm * 60 cm) - (3.14 * (7 cm)^2 * 39) ≈ 5999.14 cm^2.
Therefore, the area of the cardboard left over is approximately 5999.14 cm^2.