a) To determine how many badges can be cut from the rectangular sheet of cardboard, we need to first find the dimensions of the sheet. Let's label the length as L and the width as W.
We know that the diameter of each badge is 14 cm, which means the radius is 7 cm. To cut out a badge, we need a square of cardboard that is at least as big as the circle (so the diagonal of the square is equal to the diameter of the circle). Therefore, the side length of each square needed to cut out a badge is 14 cm (since 14 cm is the diameter of the circle).
We can fit as many squares as possible into the length and width of the cardboard. In other words, the number of squares that fit along the length of the cardboard is equal to L/14, rounded down to the nearest whole number. Similarly, the number of squares that fit along the width of the cardboard is equal to W/14, rounded down to the nearest whole number.
Therefore, the total number of badges that can be cut is:
L/14 x W/14
b) The area of the cardboard left over is equal to the total area of the rectangle minus the total area of all the badges that were cut out.
The total area of the cardboard is:
L x W
The total area of each badge is:
πr^2 = π(7 cm)^2 ≈ 153.94 cm^2
Therefore, the total area of all the badges that were cut out is:
[L/14 x W/14] x 153.94
And the area of the cardboard left over is:
L x W - [L/14 x W/14] x 153.94
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.
a) how many badges can he cut?
b) what is the area of the cardboard left over?
1 answer
1 answer