Question

The volume of a cube is 81 cubic meters. What is the volume of the square based pyramid with the same side length and height?

Answer 1

@satellite73 @Mimi_x3 @mahmit2012 Please help :D

Answer 2

@DoomDude @DeadMau5! @droiddude228 @eSpeX @egenriether Please Help me :D

Answer 3

we can do this, i just need the formula for the volume of the pyramid

Answer 4

ok give me a moment :D

Answer 5

V = 1/3B^2H

Answer 6

lets try that again.
volume is the cube of the length of the square, so the length of the side of the square is
\[\sqrt[3]{81}=3\sqrt[3]{3}\]

Answer 7

mmmm ok

Answer 8

since the height is the same as the length, we can use the formula with both \(b=3\sqrt[3]{3}\) and \(h=3\sqrt[3]{3}\)

Answer 9

ok

Answer 10

we get \[V=\frac{1}{3}(3\sqrt[3]{3})^2\times 3\sqrt[3]{3}\]
\[=\frac{1}{3}\times 27\times \sqrt[3]{3}^3=\frac{1}{3}27\times 3=27\]

Answer 11

i guess the moral of the story is that the volume of the pyramid is one third of the volume of the cube, which might have been obvious to begin with.

Answer 12

so the answer is 27?

Answer 13

that is what i get, yes.
i would not bet the ranch on it, but i am fairly sure it is right

Answer 14

Thank you soooo much!