As many 8cm diameter discs as possible are cut from a sheet of rectangular cardboard measuring 170cm by 90cm. Find the area of the sheet that is left.

The ans is 3684

Please disregard previous solution.

My theory is incorrect.

U might have done wrong calculation.

19

To find the area of the sheet that is left after cutting out the discs, we need to calculate two areas: the total area of the rectangular cardboard sheet and the total area of the discs.

1. Calculate the area of the rectangular cardboard sheet:
The rectangular cardboard sheet measures 170cm by 90cm, so its area is calculated by multiplying these two dimensions: 170cm * 90cm = 15,300 square cm.

2. Calculate the area of a single disc:
The diameter of each disc is given as 8cm, which means the radius is half of the diameter, so the radius of each disc is 8cm / 2 = 4cm.
The area of each disc can be calculated using the formula for the area of a circle: A = π * r^2.
Plugging in the value of the radius (4cm), the area of a single disc is: A = 3.14 * 4cm * 4cm = 50.24 square cm (rounded to two decimal places).

3. Determine the number of discs that can be cut from the rectangular sheet:
Since the area of the rectangular cardboard is 15,300 square cm and the area of each disc is 50.24 square cm, divide the area of the rectangular sheet by the area of a single disc to find the maximum number of discs that can be cut:
15,300 square cm / 50.24 square cm ≈ 304.46
Since we can only have whole discs, we can cut a maximum of 304 discs from the sheet.

4. Calculate the area of the discs:
Since we have 304 discs and the area of a single disc is 50.24 square cm, the total area of the discs is:
304 discs * 50.24 square cm = 15,267.52 square cm

5. Calculate the area left in the sheet:
To find the area left in the sheet, subtract the total area of the discs from the area of the rectangular cardboard sheet:
15,300 square cm - 15,267.52 square cm = 32.48 square cm

Therefore, the area of the sheet that is left is approximately 32.48 square cm.

Right so, we already know that the area of the rectangle would be 170x90=15300

And the area of one circle of diameter 8 would be;
16xpi
We can't estimate the amount of space wasted in between circles but we can tell through the diameter the amount of circles that will fit row-wise and column-wise by diving;
170/8=21.25
90/8=11.25
However since a disc can't only be .25 we take the whole number
11x21=231
231 discs will fit the rectangle completely.
Thereforth, the total area of the 231 circles would be
231x(16xpi)
And this answer should be subtracted from 15300 to obtain the wasted space.
It should roughly equal 3684-3688 depending on what value of pi you used. (i.e 22/7,3.142,pi)
Hope this helped!

Ad = pi*r^2 = 3.14 * 4^2 = 50.3 cm^2 =

Area of the disc.

Ar = 170 * 90 = 15,300 cm^2. = Area of the rectangle.

Ar/Ac=15,300/50.3=3o4.175 or 304 ciscs.

A = 0.175 * 50.3 = 8.80 cm^2 Left.