Volume of a Rectangular Prism TEKS 6.4 A/B & 6.8 A/B Lesson 8 & 9 (2nd 6 Weeks)

Volume of a Rectangular Prism The amount of space inside the prism. Volume is measured in cubic units. Formula: V = lwh V in the formula represents volume. The variable l represents length of the prism, the variable w represents the width, and the variable h represents the height.

Volume of a Cube A cube is a special rectangular prism. The length, width, and height of a cube are equal. Volume of a cube = l x w x h = s x s x s = (s³)

Volume of a cube = l x w x h = s x s x s = (s³) Hint: In order to find a missing dimension, you may need to work backwards! Multiplying the same number or variable three times is called finding the cube of the number.

We should find the formula for volume of a rectangular prism. V = lwh The volume of a rectangular prism with a width that stay the same but the length and height changes is given in the table Which expression can be used to find the volume of a rectangular prism whose width is 7 units, width is w units and length is l units? A 7 x l ÷ h B (7 + l) x h C D 7 x l x h Width (units) Length (units) Height (units) Volume (cubic units) 7 3 2 42 4 84 9 252 L W V 1. Let’s look at our 6th grade math chart to see if there is anything to help us. 4 x l We should find the formula for volume of a rectangular prism. V = lwh h

3. Let’s check to see if that is the formula they are using. A 7 x l ÷ h B (7 + l) x h C D 7 x l x h Width (units) Length (units) Height (units) Volume (cubic units) 7 3 2 42 4 84 9 252 L W V x x x x x x x x 2. We know that when variables are next to each other that it means to multiply. V= l x w x h 4 x l h 3. Let’s check to see if that is the formula they are using.

We find our choice to be D. A 7 x l ÷ h B (7 + l) x h C D 7 x l x h Width (units) Length (units) Height (units) Volume (cubic units) 7 3 2 42 4 84 9 252 L W V x x x x x x x x So it looks like we are multiplying the width by the length and height. Let’s check our answer choices to see if one of them is doing that. 4 x l h We find our choice to be D.

A cube has a side length of 4 inches A cube has a side length of 4 inches. Which of the following expressions represents the volume of the cube? A 4³ B 4 + 4 + 4 C 4 x 4 + 4 D 4 x (4 + 4) Let’s look at our 6th grade math chart to see if there is anything to help us. We should find the formula for volume of a cube. V = s³ So our answer must be A We know that s³ means s x s x s So if we replace 4 for s we would have 4³ or 4 x 4 x 4

The length of a rectangular prism is 8 units The length of a rectangular prism is 8 units. The ratio of the height to the width is 4:3. If the height is 12 units, what expression represent the volume of the prism? A. V = 8 + 9 + 12 B. V = 8 x 3 x 12 C. V = 8 x 9 x 12 D. V = 8 x 16 x 12 We know the formula for volume is V = lwh. Looking at the problem we know the length and height. We are missing the width but since it says a ratio we can make a ratio table to find the equivalent width. x 3 height 4 12 So our answer is C w 9 width 3 x 3