# Volume of Prisms

For prisms, the fastest way to find the volume is to multiply the area of the base (whatever it is) times the height.

*V* = *Bh*

That's all volume is: base times height

### Sample Problem

What is the volume of this prism?

Step 1: Find the area of the base. We're talking prisms here, so the bases are always the two parallel congruent shapes. This time around, our base shape is a triangle, so we know that the area equals half the triangle's base times the height. We only know the height of the triangle, though. Hmm, better back up a step.

Step 0: We know the height is 9 centimeters and the hypotenuse is 14 centimeters, but what about the base? Pythagorean Theorem, here we come.

*a*^{2} + *b*^{2} = *c*^{2}

(9 cm)^{2} + *b*^{2} = (14 cm)^{2}*b* ≈ 10.72 cm

Step 1: Find the area of the base...take two.

*B* = ½*bh**B* = ½(10.72 cm)(9 cm)*B* ≈ 48.24 cm^{2}

Step 2: Find the volume. In this case, the height is the length of the prism, not the height of the triangle.

*V* = *Bh**V* = (48.24 cm^{2})(12 cm)

Prepare for centimeters *cubed*.

*V* ≈ 579 cm^{3}

Awww, yeah.

If we're dealing with a cube, by the way, things get even simpler. All three dimensions of a cube are identical (length, width, and depth). So if we call our cube's side length *s*, our volume formula becomes:

*V* = *BhV* = (

*s*

^{2})

*s*

V=

V

*s*

^{3}

Yep, a cube's volume is just the side length cubed. Oh, so *that's* why raising something to the third power is called "cubing."

To mix up things a little, here's a video on the surface area and volume of a cube: