Volume of Prisms Examples

Find the volume of the prism. 

The basic formula for a prism is the area of the base times the height.

V = Bh

Since the base is a triangle, the first thing we gotta do is find the area of that triangle.

B = ½bh
B = ½(10 in)(7 in)
B = 35 in²

Now, we plug that value into the volume formula.

V = Bh
V = (35 in²)(8 in)
V = 280 in³

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, and mass is volume times density.

In order to calculate the mass of the gold block, we need to know the volume. To calculate the volume, we need to know the area of the prism's base. Well, we have to start somewhere.

The trapezoidal base can be split up into two identical right triangles and a rectangle. The area of the rectangle is length times width, or 14 meters times 16 meters.

A_rectangle = l × w = (14 m)(16 m) = 224 m²

The base of each triangle is 3 meters and the height is 16 meters.

Each triangle is 24 m², so two of them make 48 m². Adding 224 m² and 48 m² gives us 272 m² for the area of the base. Phew.

The basic volume formula is:

V = Bh

You don't have to be a rocket scientist to plug in the numbers. It might help, but you don't have to be one.

V = (272 m²)(35 m) = 9520 m³

Next is finding the mass. Since the density is given in grams per cubic centimeter, we need to convert cubic meters to cubic centimeters. That's done like this:

Now we can multiply the volume by the density to get mass. Here we go.

Mass = V × d = (9,520,000,000 cm³)(19.3 g/cm³)

Mass = 183,736,000,000 g

That's a lot of gold. We love gold.