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May 3, 201939 Insightful Publications

**Volume Of Cuboid: **You must already be aware that a solid object occupies space and the measure of the occupied space is called volume. So, the volume of the cuboid is the measure of the space occupied by the cuboid.

In this article, we will provide you with all the details regarding cuboid volume such as definition, formulas, solved examples as well as some sample questions for your practice.

Going by the definition of cuboid volume we can consider it as multiple rectangles stacked linearly to form a 3d figure and the space covered by it is given by length (l) x Breadth (b) x Height (h).

So from the above figure, we can devise another way of representing the volume i.e.

**Volume of a Cuboid = base area × height = length × breadth × height **

If the length, breadth, and height of the cuboid are equal the obtained figure is known as a cube. So, here l=b=h so we can represent these by ‘a’ as shown in the figure below:

So, computing the volume for the obtained figure we get:

** Volume of a Cube = edge × edge × edge = a ^{3}**

So now that you know what is a cube and what is a cuboid, we have provided the formulas related to both in the table that will help you in your preparation.

Cuboid | LSA: 2h(l + b)TSA: 2(lb + bh + hl)Volume: lbhl = length, b = breadth, h = height |

Cube | LSA: 4a^{2}TSA: 6a^{2}Volume: a^{3}a = side or edge of a cube |

In this section, first, we will show some solved examples and then give you practice questions as well so that you can improve your score.

**Example 1:** A wall of length 10 m was to be built across an open ground. The height of the wall is 4 m and thickness of the wall is 24 cm. If this wall is to be built up with bricks whose dimensions are 24 cm × 12 cm × 8 cm, how many bricks would be required?

**Solution 1:** Since the wall with all its bricks makes up the space occupied by it, we need to find the volume of the wall, which is a cuboid.

Here, Length (l) = 10 m = 1000 cm, Thickness (b) = 24 cm, Height (h) = 4 m = 400 cm Therefore, Volume of the wall = l × b × h = 1000 × 24 × 400 cm^{3}.

Now, each brick is a cuboid with length = 24 cm, breadth = 12 cm and height = 8 cm So, volume of each brick = l × b × h = 24 × 12 × 8 cm^{3}.

Therefore, number of bricks required = \(\frac{volume\, of\, the\, wall}{volume\, of\, each\, brick}\) => \(\frac{1000\, ×\, 24\, ×\, 400}{24\, ×\, 12\, ×\, 8}\) = 4166.6 => 4167 bricks.

**Example 2:** A child playing with building blocks, which are of the shape of cubes, has built a structure. If the edge of each cube is 3 cm, find the volume of the structure built by the child.

**Solution 2:** Volume of each cube = edge × edge × edge = 3 × 3 × 3 cm^{3} = 27 cm^{3}

- Number of cubes in the structure = 15
- Therefore, volume of the structure = 27 × 15 cm
^{3}= 405 cm^{3}.

**Volume of Cube and Cuboid Practice Questions**

Q1. A matchbox measures 4 cm × 2.5 cm × 1.5 cm. What will be the volume of a packet containing 12 such boxes? |

Q2. Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of ` 30 per m^{3}. |

Q3. A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m × 15 m × 6 m. For how many days will the water of this tank last? |

Q4. A godown measures 40 m × 25 m × 15 m. Find the maximum number of wooden crates each measuring 1.5 m × 1.25 m × 0.5 m that can be stored in the godown. |

Q5. A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid? |

Q6. A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold? (1 m^{3} = 1000 l) |

Here are some questions that are searched on the topic:

Q. What is the formula for volume of a cuboid? The formula for the volume is length x breadth x height or l x b x h or lbh.Ans. |

Q. What is volume of cube and cuboid? The formula for both cube and cuboid volumes is same i.e. length x breadth x height or lbh. However in case of cube length (l) = breadth (b) = height (h) = side (a), so volume of cube = aAns. ^{3}. |

Q. What is the meaning of volume of cuboid? It refers to the space occupied by the cuboid and is used in various applications in real life as well. The formula for the volume of cuboid is Length x Breadth X Height.Ans. |

We hope this detailed article on Volume Of Cuboid was helpful and answered all your queries. However if you have further questions feel free to use the comments section and we will provide you with an update.