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 38.99649032 badges out of the sheet of paper so what is the area of the carboard left over?
The area of the rectangular sheet of cardboard is:
100 cm x 60 cm = 6000 cm²
The diameter of each badge is 14 cm, so the radius is 7 cm. The formula for the area of a circle is:
A = πr²
Using 3.14 as pi, we get:
A = 3.14 x 7² = 153.86 cm²
To find how many badges can be cut out of the sheet, we divide the area of the sheet by the area of each badge:
6000 cm² / 153.86 cm² ≈ 38.99649032
Since Alex can only cut whole badges, he can cut out 38 badges.
The area of the cardboard used for the badges is:
38 x 153.86 cm² = 5848.68 cm²
To find the area of the cardboard left over, we subtract the area used for the badges from the total area:
6000 cm² - 5848.68 cm² = 151.32 cm²
Therefore, the area of the cardboard left over is 151.32 cm².
To find the area of the cardboard leftover, we first need to calculate the total area of the circular badges that Alex can cut out from the sheet of cardboard.
Given:
- Length of the sheet = 100 cm
- Width of the sheet = 60 cm
- Diameter of each badge = 14 cm
First, we need to find the area of one circular badge. The formula for the area of a circle is:
Area = π * (radius)^2
Since we have the diameter, we can find the radius by dividing it by 2:
Radius = diameter / 2 = 14 cm / 2 = 7 cm
Using pi (π) as 3.14, we can calculate the area of one badge:
Area of one badge = 3.14 * (7 cm)^2
= 3.14 * 49 cm^2
= 153.86 cm^2 (rounded to two decimal places)
Now, we can calculate the total area of the badges that Alex can cut out by multiplying the area of one badge by the number of badges he can make:
Total area of badges = 153.86 cm^2/badge * 38.99649032 badges
≈ 6159.81 cm^2
To find the area of the cardboard left over, subtract the total area of the badges from the total area of the sheet:
Area of cardboard left over = Total area of sheet - Total area of badges
= (Length * Width) - 6159.81 cm^2
= (100 cm * 60 cm) - 6159.81 cm^2
= 6000 cm^2 - 6159.81 cm^2
≈ 840.19 cm^2
Therefore, the area of the cardboard left over is approximately 840.19 cm^2.