can't figure out the answer to this..?

Question

i cant solve this question ..

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?

disregared the thickness of the box and round to the nearest whole number.

Answer 1

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.

Answer 2

I hope I understand this question, and I'll try to walk you through it:

1.) You're simply looking for the AREA of the half pizza, right? If so read on, if not stop reading...LOL

OK, the diameter is 50cm....you need the AREA of the Pizza HALF...

Area = Pie x r squared...which would give you the area of the HOLE pizza...you only need half so cut the answer in half by dividing by two...

As for the r in the equation, r= half the diameter...r=radius...

So half the diameter is 25, which gives you r, which you plug into the equation Area = Pie x r squared.

r squared is 625cm squared

625 times Pie (2.134...) = 1333.75cm squared.

This is the area of the hole pizza, but if I read you right you only want half the pizza, right? So divide this answer by two and you should get 666.875cm squared.

Now all you need to do is take the square root of this figure to get a square with that area, because a square has equl sides, so what times what equals 666.875cm?

the square root of 666.875 = 25.8cm, so the sides of the square that could hold the entire HALF of the pizza would be a square roughly 26cm by 26cm.

AS LONG AS YOU CAN CHANGE THE SHAPE OF THE HALF PIZZA. IF NOT, then this was/is a trick question & can only be held in a 50cm by 50cm box simply because it HAS to be as long as the longest piece and HAS to be a square box.

I hope this helps ya...if not....

OK, now what was your question again?????

Answer 3

2500 square centimetres