Answer:
Exact area = 1800 - 450pi square cm
Approximate area = 387 square cm
I used 3.14 for pi to get the approximate value.
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Explanation:
Check out the diagram below.
As the diagram shows, the largest radius possible is half of the shortest dimension of this rectangle. So the radius of each identical circle is 30/2 = 15 cm. The radius cannot exceed this value, or else the circle will spill outside the rectangle.
The area of one circle would be
A = pi*r^2
A = pi*15^2
A = pi*225
A = 225pi
Two identical circles like this combine to a total area of 2A = 2*225pi = 450pi square cm.
The area of the brown shaded region in the figure, aka the amount of cardboard leftover, is exactly 1800 - 450pi. The 1800 is from the computation of 60*30 = 1800, which is the area of the original rectangle before we made any cuts.
If we wanted to find the approximate area, then we could use pi = 3.14 to get
1800 - 450pi = 1800 - 450*3.14 = 387
The approximate area remaining is 387 square cm. This value is approximate because pi = 3.14 is approximate. If you were to use more decimal digits of pi, then you'd get some other approximate area.
