jlgdr wrote:
10^5 for volume in a cube implies 10^2*10^2*10^2 which means that the surface area of a side is 10^2. Well, we want to build the total surface area so if cube has 6 sides then 6*100 = 600. Since the area covered by each sheet is 8 , then we have 600/8 = 75 sheets needed
E
Let me know if this is clear
Cheers
J
Dear
jlgdr,
Forgive me, my friend, but I am going to correct a couple of mistakes in your approach, in an attempt to strengthen your understanding as well as the understanding of anyone else who chances upon this post.
First of all, 1 million = 1,000,000 = 10^6, not 10^5.
Second, the
1 million in this problem is
1 million liters, and the liter is a unit of volume. If you say that the cube is 10^2 = 100 on each edge, then that's 100 whats? a 100 cube-roots-of-a-liter?? You see, something becomes really funky about the units here. (In fact, a liter is a cubic decimeter, that is, a cube that is 10 cm on each side, but that would put the side of the cube at 100 decimeters, a most peculiar unit to employ.)
Finally, if the cube really were (10^2)*(10^2)*(10^2), then (10^2) would be the length of an edge, and (10^2)*(10^2) = 10^4 would be the area of a face. In general, if a cube has volume L^3, it has edge-length L, and each face has an area of L^2.
Your mistakes canceled, so you wound up with the correct answer. It's very important to appreciate when you get a question correct for correct reasons, and when you get it correct for incorrect reasons.
I hope all this helps.
Mike
_________________
Mike McGarry
Magoosh Test Prep