#38 VOCABULARY Volume is the number of cubic units needed to fill a space. Introduction 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 cm3. 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 km3 Example 4: Finding the Volume of a Triangular Prism Find the volume of the triangular prism. V = Bh 1 __ V = ( • 3.9 2 • V = 10.14 m3 1.3) • 4 Write the formula. 1 B = __ • 3.9 • 1.3; h = 4. 2 Multiply. Example 4 Example 5 1 m 2 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? FYI 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 r2, so the formula is V = Bh = r2h. 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 h +4 __ r= in., h = 9 in. 3 Example 10 Find the volume V of each cylinder to the nearest cubic unit. r = 6 ft, h = 5 ft Example 11 h r = 4 + 5, h = 8 in. 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: