Volume of Rectangular Prisms
Warm-up: What is a prism? Give several examples of a rectangular prism. Why might we need to find out how much a prism holds?
Warm-up: What is a prism? A solid figure whose bases or ends have the same size and shape and are parallel to one another, and each of whose sides is a parallelogram Give several examples of a rectangular prism. Why might we need to find out how much a prism holds?
Group Activity Use the cubes to create a rectangular shape that is 6 cubes long and 2 cubes wide. Write a formula for the area of this figure. Now stack 3 more layers on top that are identical to the first. You now have a rectangular prism. How many cubes are needed to make (fill) this prism? Write a formula for the volume of the prism.
Apply It: Jillian is building a box and wondering how much she can fit inside of it. The box is rectangular and has a base of 3 cm by 3 cm. She will make the box 4 cm tall. Use the cubes to build the base of this box. Write the formula for the area of the base of the box and find the answer. Add 3 more layers to the base. Write the formula for the volume of the box.
Volume of a Rectangular Prism V = Area of the Base x height or V = The number of cubes that fit on the bottom layer x the number of layers V = (l x w) x h
Closet Space Your relative is building a new storage closet for games and they want help in figuring out a few things. First, they need to know how much carpet they need to put on the floor of the closet, and second, they’d like to know how much space they are going to have inside for storage. The closet is 2 ½ ft x 3 ½ ft and is 6 feet high. Find the area of the floor space, then find the volume of the closet.
Warm Up Five metal cubes with sides of 5 cm are melted and casted into a spherical ball. Find the volume of the sphere that is formed. How much sand is needed to fill a pit that is 5m deep and 6m wide and 8 m long? What is the area of the bottom of that pit? What is the height of a rectangular prism with a width of 3 inches, a length of 10 inches and a volume of 210 cubic inches?
Build your own Prism Cut out the and fold your own rectangular prism. Estimate the volume of the prism in cubic centimeters. Use the cm cubes to find the number of cubes that fit into your prism. Use a ruler and Volume formula to calculate the volume of your prism in cubic centimeters. How close were your answers for #3 and #4? Explain why you think this is the case.
Warm Up How many cubic feet are in a cubic yard? Solve and draw your answer.
Warm Up A box is 3 ft by 6 ft by 9 ft. How many cubes with a side length of 3 feet will fit into the box?