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**Volume of a Rectangular Prism**

TEKS 6.4 A/B & 6.8 A/B Lesson 8 & 9 (2nd 6 Weeks)

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**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.

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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)

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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.

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**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

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**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.

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**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.

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**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 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

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**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 = 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

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