# 6th Grade - Volume Of Prisms And Cylinders

 Grade Level: 6th Skill: Geometry Topic: Volume of Prisms and Cylinders Goal: Know and use the formulas for the volume of triangular prisms and cylinders (area of base x height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid. Skill Description: Understand that volume is the measure of the amount inside a solid 3-D figure. Volume can be calculated by counting the number of cubic units needed to fill the 3-D object. Know how to find the volume of 3-D shapes by finding the area of the base and multiplying it by the height of the figure (B x h, where B represents the area of the base and h represents the height of the figure). Use the area formula for a rectangle to find the area of the base of a rectangular prism and multiply the result by the height of the figure. Understand that the formula V = l x w x h can be used to find the volume of a rectangular solid. Understand that the formula for the volume of a rectangular prism can be used to find the volume of a triangular prism. The area of a triangle is ½ the size of a rectangle, so the volume of a rectangular prism can be used and divided by 2 to find the volume of a triangular prism. To find the volume of a triangular prism use: V = lwh ÷ 2, where l and w can represent base and height of the base. Calculate the volume of a cylinder by using the area formula π r 2 and then multiplying the result by the height of the figure (V = π r 2 x h).

## Building Blocks/Prerequisites

### Sample Problems

 (1) Solve to find the volume of a rectangular prism with the length of 5 cm, width of 4 cm and height of 11 cm. (220 cm3 ) (2) Find the missing value for the rectangular prism, if: Volume: 56 cm 2 Length: 4 cm Width: 7 cm Height: ______ (2 cm) (3) Find the volume of the triangular prism, where the triangular base has a base of 3 cm and height of 5 cm. The height of the prism is 10 cm. (75 cm3 ) (4) Find the volume of a cylinder with a circular base with the radius of 7 inches and a height of 9 inches. Round your answer to the nearest one. (1385 in. 3 ) (5) Find the volume of a cylinder with a circular base with the diameter of 10 inches and a height of 12 inches. (942 in. 3 )

### Online Resources

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