Author Topic: q7 VCAA 2007 exam 1 module geometry (Read 645 times) Tweet Share

chuckjefster90 · « **on:** October 30, 2009, 09:27:41 pm »

A closed box of side length 36cm is to contain a thin straight metal rod. The maximum possible length of the rod is closest to?

a) 36cm
b) 51cm
c)62cm
d)108cm
e)216cm

i got b but answer is c

can anyone explain how they get this?

/0 · « **Reply #1 on:** October 30, 2009, 10:30:33 pm »

If you take the bottom face of the cube, the distance between opposite corners is $s = \sqrt{36^2+36^2}=36\sqrt{2}$

Now, let $s$ be the bottom side of a right angled triangle with height 36cm. The hypotenuse is the distance between furthest vertices of the cube.

This distance is $d=\sqrt{(36\sqrt{2})^2+36^2} = 36\sqrt{3} \approx 62 cm$

An easier way to do it is to apply the distance formula from coordinate geometry: $d = \sqrt{x^2+y^2+z^2} = \sqrt{36^2+36^2+36^2}$

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Author Topic: q7 VCAA 2007 exam 1 module geometry (Read 645 times) Tweet Share

chuckjefster90

q7 VCAA 2007 exam 1 module geometry

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