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Surface Area and Volume

Surface Area and Volume

At a Glance - 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:

Example 1

Find the volume of the prism. 

Example 2

Find the mass of this enormous block of gold if the density of gold is 19.3 grams per cubic centimeter. One meter equals 100 centimeters.

Exercise 1

Find the volume of the oblique prism in cubic inches.

Exercise 2

How many liters of water will fit into this swimming pool? Assume that 1 cubic foot equals about 28.3 liters. 

Exercise 3

A regular right pentagonal prism has a perimeter of 10 cm3 and a height of 8 cm3. What is its density of the prism if it weighs 110 grams? 

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