Donna wants to cut out circular discs of radius 7cm from a cardboard measuring 50cm by 70cm. What is the maximum number of circular discs that can be cut out from the cardboard?
However, all the scrap pieces cannot be used to form whole circles, so, assuming a rectangular packing of the circles, only 5 discs can be fit along the length of the cardboard. The diameter of 14 cm means that only 3 can fit across. That means that only 15 discs can be cut.
A hexagonal packing will allow for more, and I'll leave you to determine how that affects the total.
i think only 15 numbers of discs will make from this 50 x 70cm card board
To find the maximum number of circular discs that can be cut out from the given cardboard, we need to determine the most efficient way to arrange the circles within the cardboard.
First, let's calculate the area of one circular disc using the formula for the area of a circle: A = πr^2, where A is the area and r is the radius of the circle.
In this case, the radius is given as 7cm, so the area of one circular disc is A = π * 7^2 = 49π cm^2.
Next, let's calculate the area of the cardboard sheet. Given that the dimensions of the cardboard are 50cm by 70cm, the area can be calculated as A = length * width = 50cm * 70cm = 3500cm^2.
To find the maximum number of circular discs that can fit on the cardboard, we need to divide the area of the cardboard by the area of one disc. So, the maximum number of circular discs that can be cut out is:
Max number of discs = Total area of the cardboard / Area of one disc
= 3500cm^2 / 49π cm^2
Now, let's calculate this value using an approximate value for π, such as 3.14:
Max number of discs ≈ 3500cm^2 / (49 * 3.14 cm^2)
≈ 3500cm^2 / 153.86cm^2
≈ 22.71
Since we cannot have fractional or partial discs, we need to round down the final answer. Therefore, the maximum number of circular discs that can be cut out from the given cardboard is 22.
Area of disc (circle):
A = pi*r^2
A = 3.14 * 7^2
A = 153.86 cm^2
Area of cardboard (rectangle):
A = L * W
A = 70 * 50
A = 3500 cm^2
Divide area of rectangle by area of circle:
3500 / 153.86
= 22.75
Take only the whole number: 22 discs
Hope this helps :3