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Here is the question:
A Pteri with a light appetite could not finish his Rainbow Melt Pizza. In fact, he could only eat exactly half of it.
If the diameter of the pizza was 50cm, and the half-pizza was a perfect semicircle, what is the area of the smallest square box, in square centimetres, that could contain the half pizza? Please disregard the thickness of the box, round to the nearest whole number, and please only submit a number for your answer.
2007-10-31 16:38:50 · 7 answers · asked by Aqwah 1 in Science & Mathematics ➔ Mathematics
Imagine starting by putting the diameter of the semicircle directly in the corner of a square but at a 45 degree angle. That makes a 45-45-90 triangle with the hypotenuse being 50 cm.
Now take the midpoint of this and draw your semicircle. The distance from this point up will be the radius (25 cm). And down will be the side of a triangle with hypotenuse 25. This ends up being 25/√2.
So one dimension would be 25 + 25/√2, and so would the other. Multiplying this together we get:
(25 + 25/√2)²
= 25² + 50*25/√2 + (25/√2)²
= 625 + 1250/√2 + 625/2
≈ 625 + 883.883 + 312.5
≈ 1821 sq. cm
I drew the following diagram to help explain things.
2007-11-01 20:56:49 · answer #1 · answered by Puzzling 7 · 0⤊ 0⤋
50*50=2500
since the diameter is 50 and you want the are of the smallest "square" box it has to be 50cmx50cm
2007-10-31 20:20:19 · answer #2 · answered by Anonymous · 0⤊ 1⤋
L = 50, W = 25
area = 50 x 25
=1250cm sq
2007-10-31 16:44:50 · answer #3 · answered by PELANGI 2 · 0⤊ 2⤋
yes 2500 because it asks for the smallest SQUARE box L = W= 50 50^2 is 2500
2007-10-31 16:54:06 · answer #4 · answered by Wolf of the Red Moon 5 · 0⤊ 2⤋
2500
2007-11-01 07:13:42 · answer #5 · answered by Anonymous · 0⤊ 1⤋
1250sq.cm
2007-10-31 16:48:42 · answer #6 · answered by melville tiger 2 · 0⤊ 2⤋
2,500.
2007-10-31 16:47:01 · answer #7 · answered by The Camel 4 · 0⤊ 2⤋