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Surface Area and Volume

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.

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(9 cm)(10.72 cm)
B ≈ 48.26 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 = (48.26 cm2)(12 cm)

Prepare for centimeters cubed.

V ≈ 579 cm3

Awww, yeah.

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

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