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How much water will need to be added to a rectangular prism to fill it up completely if the box measures 4 cm by 5 cm and is 6 cm tall. There is another solid rectangular prism found inside the box that measures 2 cm by 3 cm and is 3 cm tall.

Find the volume of the original prism.
4 x 5 x 6 = 120 cm cubed

Subtract the volume of the solid prism
2 x 3 x 3 = 18 cm cubed
120-18= 102 cm cubed 

rectangular prism with another rectangular prism inside
Problem 1. Find the volume of a rectangular prism that has a base of 4 units and 7 units, and a height of 5 units.

Step 1. Use the formula for finding volume which equals V= Ba * h
  Ba = Base Area
  H = height

Step 2. Find the base area of a rectangle Ba = Length x Width
  4* 7 = 28 units

Step 3. Multiply the Ba * height
  28 * 7 = 140 units cubed 
rectangular prism

Volume of a Rectangular Prism

A prism is a three dimensional figure with two faces that are congruent and sides that are parallelograms. A prism is named after the shape of the two identical faces or bases. A rectangular prism has two faces in the shape of a rectangle. Some common examples of rectangular prisms in real life are, cereal boxes, Kleenex boxes, shipping containers, dice, and aquariums. 

One can find the volume of a rectangular prism by using the formula:

Volume of rectangular prism = Base area times the height

Base area = length of the prism times the width

Which side is the height? 

Any side can be used as the height with a rectangular prism. 
Let’s investigate why?
Suppose you have a rectangular prism with sides of 3 units,4 units, and 6 units.
  • Using the volume rectangular prism formula: base area * height
  • Using the side of 4 units as the height 6 x 3 = 18 x 4 = 72 units cubed
  • Using the side of 3 units as the height 4 x 6 = 24 x 3 = 72 units cubed
  • Using 6 units as the height 4 x 3 =12 x 6 = 72 units cubed

rectangular prism 3x4x6
If you know the volume of the rectangular prism, and the base area you can also find the height.

Find the height of a rectangular prism with a volume of 60 units cubed, and a side length of 4 units and a height of 5 units.

Volume = base area * height
To find the base area = 4*5 = 20
60 = 20 * x
x =3 height = 3 units 

Volume of a Rectangular Prism word problems

John wants to know the volume of an odd shaped rock he found. He places the rock in a rectangular cylinder filled with water that measures 10 cm by 8cm. After placing the rock in the water, the volume of the water rises 3 cm.

The volume of the rock will equal to the amount of water increase.
To find this increase we will use base area x height.
Base area equals length x width or 10 x4 =40 cm.
The water rises 3 cm so we can use this as the height giving us 40 x 3 = 120 cm cubed as the volume of the rock.

rectangular prism with a rock submerged

Example problem finding rectangular prism volume.

Common Core Standard   6.G.2    7.G.6 

6th Grade Math       7th Grade Math