Remember Your Geometry?

Can a 24 inch-long flute fit into a box measuring 12 inches by 14 inches by 16 inches? If no, why not. If yes, explain.

Yes since the square root of (12^2 + 14^2 + 16^2) = 24.4.

Also, flutes come apart.

:-)

Originally posted by wittywonka
Can a 24 inch-long flute fit into a box measuring 12 inches by 14 inches by 16 inches? If no, why not. If yes, explain.

Not without taking it apart or snapping it in half. I think the longest line inside the box from bottom corner to its opposite top corner would be 21.26 inches. I'm probably missing something, but I'm going with my frist instinct 🙂

Originally posted by jebry
Yes since the square root of (12^2 + 14^2 = 16^2) = 24.4.

Also, flutes come apart.

:-)

Actually I think your right, I didn't use three dimensional math. My bad.

three dimensional math

That's the key...nicely done

Originally posted by wittywonka
That's the key...nicely done

It's going to depend on the width of the flute - you don't get to use the full diagonal of the box until the flute has pointed ends.

yes, because there is enough room.

Alrighty, here's yet another geometry problem, much harder. What is the circumference of a circle inscribed in an equilateral triangle with a height of (12 * square root of 3)?

Originally posted by wittywonka
Can a 24 inch-long flute fit into a box measuring 12 inches by 14 inches by 16 inches? If no, why not. If yes, explain.

The answer is yes. And it is nicely shown.

Part 2 of the same problem is:
What diameter can the flute have in order to fit in that box?
(Suppose that the flute is cylindrical.)

Somewhat harder problm, don't you think?

8 x pi x rt3

Originally posted by wittywonka
Alrighty, here's yet another geometry problem, much harder. What is the circumference of a circle inscribed in an equilateral triangle with a height of (12 * square root of 3)?

24xpi/(sqrt3)

Originally posted by wittywonka
Alrighty, here's yet another geometry problem, much harder. What is the circumference of a circle inscribed in an equilateral triangle with a height of (12 * square root of 3)?

That's not hard.

The inscribed circle of an equilateral triangle is centred on the triangle's centre. The triangle's centre is situated 1/3rd of the way along each of the triangle's three height lines. The radius of the circle is equal to the distance of the centre, along the height line, to the nearest side of the triangle. All these are easily seen when you draw a diagram, and flow elementarily from the equilaterality of the triangle.
The radius of the circle is, then, a third of 12*sqrt(3), is 4*sqrt(3). It circumference is therefore 2 pi r, equals 2 pi 4 sqrt(3), equals 8 pi sqrt(3). Its area is more interesting; that's pi r**2, which is pi 4**2 sqrt(3)**2, equals pi * 16 * 3, equals 48 pi, eliminating the square root.

Richard

shallow blue is reatarded i think in my memory, but here's my answer.

12*sqrt3*2/3pi=8*sqrt3*pi

Originally posted by FabianFnas
The answer is yes. And it is nicely shown.

Part 2 of the same problem is:
What diameter can the flute have in order to fit in that box?
(Suppose that the flute is cylindrical.)

Somewhat harder problm, don't you think?

i'll be glad if you show me the answer and how to do it

nevermind i think i know how to do it

at the rectangle box the corner is where the flute ends

the flute is allowed with 24.4131112315...and it's 24in long. therefore the allowed space on each side is .4131112315/2 in long.

when the diameter cuts, the leftover area become a rect prism with side lenth RATIO of 12:14:16 cuted in half. therefore .4131112315 is the diagnal of rectangle diamention ratio of 6:7:8.

since the maxium diameter creates a circle that slices the little rect prism in half, it's diameter is equal to the diagnal of the little cube. so the diameter maxium allowed is 0.4131112315 inches, about 1 centimeter.