Old Mother Hubbard
Looked in her cupboard
To get her dog a bone
But when she got there
She saw a small square
A cube for Fido to much on!
So, she was quite pleased
But then her dog wheezed
And she started to wonder:
Did the cube have enough
Nutrients and stuff
So that her dog will recover?
As poor Mother Hubbard did her research, she learned the cube is one of the friendliest shapes in all of mathematics.
A cube is a square in three dimensions. Like this:
As we all know, a square is made up of FOUR equal sides. A cube is made up of 6 squares, with four on the sides, one on the top, and one on the bottom.
Volume is basically Length times Width times Height, or:
V = L x W x H
That’s a lot easier than calculating the volume of a sphere. Since every side of a cube is the same, knowing one side will let us know all three and finally, volume of a cube! Like so:
Fill in the values:
V = L x W x H
V = 15cm x 15cm x 15xm
V = 3375 cm3
Don’t forget the 3 since we are discussing three dimensions!
***Let’s make it a little harder, just for fun!
Say we only had the diagonal of one side of the square! What do we do?!?!?
We’ll say that Line DB has a value of 16 cm.
We can use the Pythagorean Theorem!
The theory is for a right triangle, which we have. It’s just a rectangle divided in half along its diagonal. Like this:
The theorem states that a2 + b2 = c2
This is pretty easy, since we know that, in a square, the two sides (a and b) are the same length! If it doesn’t seem easy, we can help simplify the process with some equations homework help.
So a2 + a2 = c2
2a2 = c2We know that our diagonal in this case is 16.
2a2= 162
2a2 = 256
a2= 128
a = 11.31cm
Once we know the side of one square, we can simply plug it into the formula for volume…
V = L x W x H
V = 11.31cm x 11.31cm x11.31cm
V = 14476.73cm3
If Ol’ Mother Hubbard found a RECTANGULAR PRISM she could use the same cube formula to find volume! Or she could just talk to an online math tutor.
V = L x W x H
V = 6cm x 4 cm x 5 cm
V = 120cm3
Armed with this knowledge, Mother Hubbard is ready to take the Fido to the next level!