Rectangular prism unit cubes

Rectangular prism unit cubes DEFAULT

Volume of Rectangular Prisms – Explanation & Examples

The volume of a rectangular prism is the measure of the space the fills it. In this article, you will learn how to find a rectangular prism volume by using the volume of a rectangular prism formula. We will also discuss the volume of a spherical cylinder.

How to Find the Volume of a Rectangular Prism?

A rectangular prism is a 3-dimensional object with six rectangular faces. A rectangular prism is also referred to as a cuboid, rectangular hexahedron, right rectangular prism, or a rectangular parallelepiped.

To find the volume of a rectangular prism, multiply the length, width, and height. The unit for measuring the volume of a rectangular prism is cubic units, i.e., cm3, mm3, in3, m3, etc.

Volume of a Rectangular Prism Formula

The formula for the volume of a rectangular prism is given as:

Volume of a rectangular prism = (length x width x height) cubic units.

V = (l x w x h) cubic units

In a rectangular prism, the product of the length and the width is known as the base area. Therefore, we can also represent the volume of a rectangular prism formula as:

Volume of a rectangular prism = Base area x height

Let’s try the formula by working out a few example problems.

Example 1

The length, width, and height of a rectangular prism are 15 cm, 10 cm, and 5 cm, respectively. What is the volume of the prism?

Solution

Given, length = 15 cm,

width = 10 cm,

height = 5 cm.

By the volume of a rectangular prism, we have

Volume = l x w x h

= (15 x 10 x 5) cm3

= cm3.

Example 2

The volume of a rectangular prism is cm3. If the prism&#;s length is twice the height and width of 6 cm, find the dimensions of the rectangular prism.

Solution

Given,

Let the height be x.

Length = 2x

Width = 6 cm.

Volume =

By volume of a rectangular prism,

⇒ = x(2x) (6)

⇒ = 12x2

On dividing both sides by 12, we get

⇒ 16 = x2

⇒ x = 4, -4

Substitute

Length = 2x ⇒ 2x 4 =8 cm

Height = x ⇒ 4 cm

Therefore, the dimensions of the rectangular prism are 8cm, 6cm, and 4 cm.

Example 3

The length and width of a rectangular aquarium are mm and mm. When fish is introduced in the aquarium, the water level rises by mm. Find the volume of the fish.

Solution

The volume of the fish = the volume of the water displaced.

Volume of the fish = x x mm3

= x 107 mm3

Example 4

A rectangular water tank is 80 m long, 50 m wide, and 60 m in height. If the water&#;s depth in the tank is 45 m, find the volume of water required to fill the tank?

Solution

To find the water volume needed to fill the tank, subtract the available water volume from the volume of water when the tank is full.

Volume of water, when the tank is full = 80 x 50 x 60

= , m3

Volume of the water available = 80 x 50 x 45

= , m3

Volume of the water required = (, &#; ,) m3

= 60, m3

Example 5

The volume and base area of a rectangular cargo container is m3 and m2. Find the height of the container?

Solution

Volume of a rectangular prism = base area x height

= x height

Divide on both sides.

/ = height

height = m

So, the height of the container is m.

Example 6

Small boxes of dimension 1 m x 4 m x 5 m are to be packed in a larger rectangular container of dimension 8 m x 10 m x 5 m. Find the maximum number of small boxes that can be packed in the container?

Solution

To find the number of boxes to be packed, divide the container&#;s volume by the volume of the box.

Volume of the container = 8 x 10 x 5

= m3.

Volume of box = 1 x 4 x 5

= 20 m3

Number of boxes = m3/20 m3.

= 20 boxes.

Example 7

The external dimensions of a wooden box which is open at the top is given as 12 cm long, 10 cm wide and by 5 cm height. If the walls of the box are 1 cm thick, find the volume of the box

Solution

Find the internal dimensions of the box

Length = 12 – (1 x 2)

= 10 cm

Width = 10 – (1 x 2)

= 8 cm

Height = 5 cm – 1 …… (open at the top)

= 4 cm

Volume = 10 x 8 x 4

= cm3.

Example 8

What are the dimensions of a cube with the same volume as a rectangular prism with the dimensions as 8 m by 6 m by 3 m?

Solution

Volume of a rectangular prism = 8 x 6 x 3

= cm3

So, a cube will also have a volume of cm3

Since we know that the volume of a cube = a3

where a is the length of a cube.

= a3

3√ a3 = 3

a =

Therefore, the dimensions of the cube will be cm by cm by cm.

Example 9

Calculate the volume of a solid rectangular prism whose base area is 18 in2 and height is 4 in.

Solution

Volume of a rectangular prism = length x width x height

= base area x height

V= 18 x 4

= 72 in3.

Example 10

Find the base area of a rectangular prism whose volume is cm3 and height is 18 cm.

Solution

Volume = base area x height

= base area x 18

By dividing both sides by 18, we get

Base area = cm2

Practice Questions

  1. How do you identify a prism?

A. It has length, height, and width of equal or unequal lengths.

B. It has length, height, and width of unequal lengths.

C. It has length, height, and width of equal or unequal lengths.

D. None of these.

2. Which of the following is not a prism?

A. Tissue box

B. Football

C. Dice

D. None of these

3. How many cubic meters of water a rectangular prism-shaped swimming pool can hold, which is 12 meters long, 5 meters wide, and meters deep?

4. James has a music box with a height of cm and a base area of 75 square cm. Find the volume of the musical box.

Answers

  1. C
  2. B
  3. 90 cubic meters
  4. 5 cubic cm

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How many unit cubes are in a rectangular prism?

In other words, it is five cubes long, by two cubes high by one cube wide. You can multiply each of these values together to get the volume of the rectangular prism. The volume of the rectangular prism is 10 cubic units or units3.

Click to see full answer.


Accordingly, how many cubes are needed to fill a rectangular prism?

It takes 64 – ¼ inch cubes to fill one unit cube. The right rectangular prism can be filled with ¼ inch cubes. It takes 9 x 2 x 4 cubes to fill this right rectangular prism. It takes 72 – ¼ inch cubes to fill this right rectangular prism.

Secondly, how many rectangular prisms can 20 unit cubes make? Explanation: Look at the factors of 20 . They are 1,2,4,5,10and20 . Hence, Chloe can build 4 different rectangular prisms with 20 unit cubes.

Also know, how many 1/4 unit cubes does it take to fill the prism?

Each cube with side lengths of 1/4 have a volume of (1/4)3 which means each cube's volume is cubic units. To find how many cubes are needed to fill the prism, divide 3 cubic units by cubic units. Your answer will be cubes. Rose S.

What is the formula for volume?

Calculating VolumeThe formula to find the volume multiplies the length by the width by the height. The good news for a cube is that the measure of each of these dimensions is exactly the same. Therefore, you can multiply the length of any side three times. This results in the formula: Volume = side * side * side.

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Unit rectangular cubes prism

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Volume with Unit Cubes (Missing Cubes)

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