Surface Area and Volume
Topics
Introduction to :
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 = ½bh
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: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 cm^{3} and a height of 8 cm^{3}. What is its density of the prism if it weighs 110 grams?