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.
Any help on how to solve this would be great, as my math skills are a bit rusty.
2007-11-01 04:56:33 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Imagine starting by putting the diameter of the pizza directly in the corner of a box 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
≈ 1821.383 sq. cm
Since they want us to round to the nearest whole number, the answer is 1821 sq. cm
I drew the following diagram to help explain things.
2007-11-01 05:02:32 · answer #1 · answered by Puzzling 7 · 0⤊ 1⤋
2
2007-11-04 09:18:50 · answer #2 · answered by Camila M 1 · 0⤊ 0⤋
diameter is 50 cm... and it is a semicircle...
for a perfect square box, u have no choice but to use a 50x50 square box... giving the area of 50x50=2500cm^2
2007-11-01 12:13:40 · answer #3 · answered by Anonymous · 0⤊ 2⤋