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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.

a2 + b2 = c2
(9 cm)2 + b2 = (14 cm)2
b ≈ 10.72 cm

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

B = ½bh
B = ½(10.72 cm)(9 cm)
B ≈ 48.24 cm2

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 cm2)(12 cm)

Prepare for centimeters cubed.

V ≈ 579 cm3

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 = Bh
V
= (s2)s
V
= s3

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: