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# Surface Area and Volume

# 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. It's a triangle, so we know that the area equals half the base times the height. We only know the height.

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(9 cm)(10.72 cm)*B* ≈ 48.26 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* = (48.26 cm^{2})(12 cm)

Prepare for centimeters *cubed*.

*V* ≈ 579 cm^{3}

Awww, yeah.

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