Definition and Properties of Volume

New York State Common Core Math Geometry, Module 3, Lesson 8

Worksheets for Geometry

Student Outcomes

• Students understand the precise language that describes the properties of volume.
• Students understand that the volume of any right cylinder is given by the formula area of base×height.

Definition and Properties of Volume

Classwork

Opening Exercise

a. Use the following image to reason why the area of a right triangle is 1/2𝑏ℎ (Area Property 2).
b. Use the following image to reason why the volume of the following triangular prism with base area 𝐴 and height ℎ is 𝐴ℎ (Volume Property 2).

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Exercises

Complete Exercises 1–2, and then have a partner check your work.

1. Divide the following polygonal region into triangles. Assign base and height values of your choice to each triangle, and determine the area for the entire polygon.
2. The polygon from Exercise 1 is used here as the base of a general right prism. Use a height of 10 and the appropriate value(s) from Exercise 1 to determine the volume of the prism.
3. A square metal plate has a density of 10.2 g/cm³ and weighs 2.193 kg.
   a. Calculate the volume of the plate.
   b. If the base of this plate has an area of 25 cm², determine its thickness.
4. A metal cup full of water has a mass of 1,000 g. The cup itself has a mass of 214.6 g. If the cup has both a diameter and a height of 10 cm, what is the approximate density of water?

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