9-6 Volume of Prisms
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Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
9-6 Volume of Prisms
Warm UpFind the area of each figure. Use 3.14 for .
96 in2
50.24 ft2
1. rectangle with base length 8 in. and height 12 in.
2. circle with diameter 8 ft
9-6 Volume of Prisms
Problem of the Day
A rectangular park is bordered by a 3-foot-wide sidewalk. The park, including the sidewalk, measures 125 ft by 180 ft. What is the area of the park, not including the sidewalk?20,706 ft2
Volume of Prisms
9-6 Volume of Prisms
MA.6.G.4.3 Determine the missing dimension of a prism…given its volume…or the volume given the dimensions.
Also MA.6.A.3.4
Sunshine State Standards
9-6 Volume of Prisms
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.
9-6 Volume of Prisms
Additional Example 1: Finding the Volume of a Rectangular Prism
Find the volume of the rectangular prism.
V = lwh Write the formula.
V = 26 • 11 • 13 l = 26; w = 11; h = 13
Multiply.V = 3,718 in3
9-6 Volume of Prisms
Check It Out: Example 1A
Find the volume of each rectangular prism.
V = lwh = 2 × 3 × 8 = 48 ft 3
9-6 Volume of Prisms
Check It Out: Example 1B
Find the volume of each rectangular prism.
V = lwh = 1 × 1 × 2 = 2 km3
9-6 Volume of Prisms
Check It Out: Example 1C
Find the volume of each rectangular prism.
V = lwh = 8.4 × 5.1 × 6 = 257.04 in 3
9-6 Volume of Prisms
To find the volume of any prism, you can use the formula V= Bh, where B is the area of the base, and h is the prism’s height.
9-6 Volume of Prisms
Additional Example 2: Finding the Volume of a Triangular Prism
Find the volume of thetriangular prism.
V = Bh Write the formula.
V = ( • 3.9 • 1.3) • 412__ B = • 3.9 • 1.3; h = 4.1
2__
Multiply.V = 10.14 m3
9-6 Volume of Prisms
Additional Example 3: Problem Solving Application
Suppose a facial tissue company ships 16 cubic tissue boxes in each case. What are the possible dimensions for a case of tissue boxes?
11 Understand the ProblemThe answer will be all possible dimensions for a case of 16 cubic boxes.
List the important information:
• There are 16 tissue boxes in a case.
• The boxes are cubic, or square prisms.
9-6 Volume of Prisms
You can make models using cubes to find the possible dimensions for a case of 16 tissue boxes.
22 Make a Plan
Additional Example 3 Continued
9-6 Volume of Prisms
Solve33
You can make models using cubes to find the possible dimensions for a case of 16 cubes.
Additional Example 3 Continued
The possible dimensions for a case of 16 cubic tissue boxes are the following: 16 x 1 x 1, 8 x 2 x 1, 4 x 4 x 1, and 4 x 2 x 2.
9-6 Volume of Prisms
Notice that each dimension is a factor of 16. Also, the product of the dimensions (length • width • height) is 16, showing that the volume of each case is 16 cubes.
Look Back44
Additional Example 3 Continued
9-6 Volume of Prisms
Check It Out: Example 3A 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?
The original volume is 3 × 2 × 2 = 12 ft . 50% of 12 is 6, so the longer toy box has a volume of 12 + 6 = 18 ft . So L × 2 × 2 = 18, and L = 18 ÷ 4 = 4.5. The length of the longer toy box is 4.5 feet.
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