Question

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.

Answer 1

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.

Answer 2

Please disregard previous solution.
My theory is incorrect.

Answer 3

The ans is 3684

Answer 4

U might have done wrong calculation.

Answer 5

19

Answer 6

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!