 # The Volume of a Right Prism - Capacity

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Lesson Plans and Worksheets for Grade 7
Lesson Plans and Worksheets for all Grades

Examples, videos, and solutions to help Grade 7 students learn how to use the formula to find the volume of a right rectangular prism.

### Lesson 24 Student Outcomes

• Students use the formula for the volume of a right rectangular prism to answer questions about the capacity of tanks.
• Students compute volumes of right prisms involving fractional values for length.

Lesson 24 Classwork

Example 1: Measuring a Container’s Capacity
A box in the shape of a right rectangular prism has a length of 12 in., a width of 6 in., and a height of 8 in. The base and the walls of the container are 1/4 in. thick, and its top is open. What is the capacity of the right rectangular prism? (Hint: The capacity is equal to the volume of water needed to fill the prism to the top.)

Example 2: Measuring Liquid in a Container in Three Dimensions
A glass container is in the form of a right rectangular prism. The container is 10 cm long, 8 cm wide, and 30 cm high. The top of the container is open and the base and walls of the container are 3 mm (or 0.3 cm) thick. The water in the container is 6 cm from the top of the container. What is the volume of the water in the container?

Example 3
7.2 L of water are poured into a container in the shape of a right rectangular prism. The inside of the container is 50 cm long, 20 cm wide, and 25 cm tall. How far from the top of the container is the surface of the water? (1L = 1000 cm3)

Example 4
A fuel tank is the shape of a right rectangular prism and has 27 L of fuel in it. It is determined that the tank is 3/4 full. The inside dimensions of the base of the tank are 90 cm by 50 cm. How deep is the fuel in the tank? How deep is the tank? (1L = 1000 cm3)

Closing
• How do containers, such as prisms, allow us to measure the volumes of liquids using three dimensions?
• When liquid is poured into a container, the liquid takes on the shape of the container’s interior. We can measure the volume of prisms in three dimensions, allowing us to measure the volume of the liquid in three dimensions.
• What special considerations have to be made when measuring liquids in containers in three dimensions?
• The outside and inside dimensions of a container will not be the same because the container has wall thickness. In addition, whether or not the container is filled to capacity will affect the volume of the liquid in the container. 