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**Volume of 3-Dimensional Figures**

Cubes and Rectangular Prisms

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Volume of Cubes All of the sides of a cube are in the shape of a square. In a square, all of the sides are the same length. To find the volume, simply multiply the length by the width by the height. These dimensions are the same number. So we use the following formula. V = s3 s s s

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**Example Find the volume of the following cube.**

To find the volume of a cube, just multiply all 3 numbers. 6 x 6 x 6 gives us the volume. 6 x 6 = 36 and 36 x 6 = 216 Thus, the volume is 216 ft3 Notice that the unit of measurement is cubed. The shape has 3 dimensions so it is cubed.

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**YOUR TURN!!! Find the volume of the cube.**

Take the 3 dimensions and multiply them. 3 x 3 x 3 = 27 So the volume of the cube is 27 yd3 3 yd 3 yd 3 yd

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**Volume of Rectangular Prisms**

With the key word being rectangular, recall that the area is length x width. You will use this to find the volume of a rectangular prism. Remember that a rectangle has opposite sides congruent. So the numbers will not be the same. To find the volume simply use the following formula. V = lwh

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**Example Find the volume of the rectangular prism.**

To find the volume, multiply all 3 dimensions. V = 4 x 11 x 2 4 x 11 = x 2 = 88 Thus, the volume is 88 m3

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**NOW YOU TRY Find the volume of the rectangular prism. V = 5 x 8 x 18**

The volume is 720 cm3 18 cm 5 cm 8 cm

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SAMPLE ARMT QUESTION How many 1-centimeter cubes will be needed to completely fill the empty rectangular prism shown below. 18 cm 5 cm 7 cm

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**Sample ARMT Question Cont.**

First, find the volume of the rectangular prism. V = lwh, so V = 7 x 5 x 18. This equals 35 x 18 which equals So, the volume is 630 cubic centimeters. Since each cube has a volume of 1 cubic centimeters, then it will take 630 cubes to completely fill the prism. In conclusion, find the volume of the prism. Then, take the volume of the cube and divide it into the volume of the prism.

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**Summary The dimensions of a cube are the same number.**

The dimensions of a rectangular prism are different. Only the opposite side measurements are the same. To find the volume of a cube or a rectangular prism, just multiply all 3 dimensions. V = lwh This works for both cubes and prisms.

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