Volume of a Cube and Rectangular Prism

Transcription

1 Distance Education for Elementary Schools Self- Instructional Materials Volume of a Cube and Rectangular Prism Skill: Department of Education BUREAU OF ELEMENTARY EDUCATION 2 ND Floor Bonifacio, Building Dep Ed Complex, Meralco Avenue Pasig City

2 VOLUME OF A CUBE AND RECTANGULAR PRISM Objective: Find the volume of a cube or rectangular prism Review Find the area of the following figures. Write the answer on your notebook. 6 m 9 m 10 m 4 m 4) 5) 4 m 3 m 4 m 7 m Study and Learn Before we proceed to explore the volume of a rectangular prism, let us see what a prism is. Prism is a solid with two bases that are parallel and identical polygons. These are the examples of a prism. bases bases bases rectangular prism square prism or cube triangular prism 1

3 Are the two bases in each solid parallel? Are the bases identical polygon? Now that you know what a prism is, we will proceed to our lesson. Read the following problem. A box is 10 cm long, wide and tall. What is its volume? Let us visualize the problem. height width 10 cm length - cubic centimetre 1 cm 3 A cube has 3 dimensions: length, width and height. It is the unit used for measuring volume. Volume is expressed in cubic units. The number of cubic units needed to make or fill a solid figure is called the volume. We write cubic units: unit 3. The figure above is a box whose dimensions are 10 cm long, wide and 3 cm high. To find the volume, we need to know the number of cubes in the whole figure. We know that the bottom of the prism is 10 centimetres long and 5 centimetres wide and that it is also 3 cubes high. To find the total number of centimeter cubes, We multiply to find the number of cubes on the bottom layer. Then multiply by the number of layers We multiply 10 by 5 by x 5 x 3 = 150 centimetre cubes length width height number of cubes on bottom layer number of layers The volume of the box is 150 cm 3. 2

4 So, the formula in finding the volume of a rectangular prism is: Volume = length x width x height In symbols: V = l x w x h, we may also use the general formula V = b x h, where b stands for the area of the base Therefore, we can use the formula, V = l x w x h or V = b x h in finding the volume of a rectangular prism. Let us take a look at some more examples. Study the figures below. 4 m 2 cm 6 m 10 m V =? V =? V =? V = l x w x h = x x 2 cm = 30 cm 3 V = b x h = (10 m x 6 m) x 4m = 60 m 2 x 4 m = 240 m 3 V = l x w x h = x x = 2 3 The solid figure in numbers 1 and 2 are both rectangular prisms. The third figure is also a prism but since the length, width and height are all the same, it has a special name. It is called a cube. If the length, width and height of a cube are all equal, we can substitute s for length, width and height and form a specific formula for finding the volume. V = l x w x h s s s V = s x s x s V = s 3 (the formula for the volume of a cube) Example: Find the volume of a cube whose side is 4 dm. 3

5 Solution: V = s3 = (4 dm) 3 = (4 dm) (4 dm) (4 dm) = (16 dm2)(4 dm) V = 64 dm 3 Note: Some use e for edge instead of s for side. So you may also encounter the formula V = e3 for cube. It is important to remember to express volume in cubic units. Try These A. Find the volume of the following prisms. Write the answers in your notebook. 12 cm 4 cm 20. 4) 5) 6 cm 14 cm 14 cm 14 cm B. Solve each problem. Write your solution on your notebook and encircle your final answer. 1. A storage box is 50 cm by 30 cm by 40 cm. What is the volume of the box? 2. Find the volume of a cube whose side is 4.3 dm. 4

6 Wrap Up Prism a solid with two bases that are parallel and identical polygons. Ex. Rectangular prism, square prism, triangular prism. Cubic unit the unit used to find the volume of a solid Volume the number of cubic units needed to fill a solid figure. The formula for finding the volume of: Rectangular prism: V = l x w x h Square prism or cube: V = s 3 or V = e 3 The General Volume Formula for any prism is: V = b x h, where b stands for the area of the base On Your Own A. Find the volume of the following prism. Write your answer on your notebook. 2 cm 2 cm 1 9 cm ) 5) 11 cm 1 31 cm 1 1 5

7 B. Find the volume of each prism. Write your answer on your notebook. 12 cm 12 cm 2 cm 4) 5) 1 12 cm 4 cm Check your answer with the answer key. If you get 8-10 Excellent! You may now proceed to the next lesson. 5-7 You need to review the processes you missed. 0-4 You need to repeat the whole process. Ask your teacher or elder to help you. 6

8 Key to Correction COMPREHENSION OF VOLUME REVIEW 1) 54 m 2 2) 25 m 2 3) 40 m 2 4) 16 m 2 5) 21 m 2 TRY THESE A. B. 1) 180 cm 3 1) cm 3 2) 574 cm 3 2) dm 3 3) 336 cm 3 4) 512 cm 3 5) 2744 cm 3 ON YOUR OWN A. B. 1) ) 120 cm 3 2) 60 cm 3 2) 480 cm 3 3) ) ) ) ) ) 720 cm 3 7