# #38. Volume is the number of cubic units needed to fill a space. VOCABULARY.

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#38

Volume is the number of cubic units needed to fill a space. VOCABULARY

You need 10, or 5 · 2, centimeter cubes to cover the bottom layer of this rectangular prism. You need 3 layers of 10 cubes each to fill the prism. It takes 30, or 5 · 2 · 3, cubes. Volume is expressed in cubic units, so the volume of the prism is 5 cm · 2 cm · 3 cm = 30 cm 3. Introduction

Example 1: Finding the Volume of a Rectangular Prism Find the volume of the rectangular prism.

Example 2 Find the volume of each rectangular prism. 3

Example 3 Find the volume of each rectangular prism. V = lwh = 1 × 1 × 2 = 2 km 3

Example 4: Finding the Volume of a Triangular Prism Find the volume of the triangular prism. V = BhWrite the formula. V = ( 3.9 1.3) 4 1 2 __ B = 3.9 1.3; h = 4. 1 2 __ Multiply.V = 10.14 m 3

Example 4

Example 5 2 1 m

Example 6

Example 7 A toy box is a rectangular prism that is 3 ft long, 2 feet wide, and 2 feet tall. Another toy box has the same dimensions, except that it is longer. If the longer toy box has a volume that is 50% greater than the original toy box, what is the length of the longer toy box?

To find the volume of a cylinder, you can use the same method as you did for prisms: Multiply the area of the base by the height. volume of a cylinder = area of base  height The area of the circular base is r 2, so the formula is V = Bh = r 2 h. FYI

Example 8: Finding the Volume of a Cylinder Find the volume V of the cylinder to the nearest cubic unit. r = 4 ft, h = 7 ft

Example 9: Finding the Volume of a Cylinder r = in., h = 9 in. + 4 h 3 __

Example 10 Find the volume V of each cylinder to the nearest cubic unit. r = 6 ft, h = 5 ft

Example 11 r = + 5, h = 8 in. h 4

Example 12 Sara has a cylinder-shaped sunglasses case with a 3 in. diameter and a height of 6 in. Ulysses has a cylinder-shaped pencil holder with a 4 in. diameter and a height of 7 in. Estimate the volume of each cylinder to the nearest cubic inch. Sara’s sunglasses case

Example 13 Ulysses’ pencil holder

Example 14: Comparing Volumes of Cylinders Find which cylinder has the greater volume. Cylinder 1: Cylinder 2:

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