Volume formulas and solved examples for 3D shapes
The volume of an object or a closed surface is a mathematical quantity that shows how often three-dimensional space it occupies. The volume is measured in cubic units such as m3, cm3, and so on.
Volume is sometimes spoken to as capacity. The volume of a cylindrical jar, for example, is used to calculate how much water it can contain.
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Volume of Cuboid
A cuboid is a solid geometrical object with 6 faces.
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Volume of the cuboid(V) = length × breadth × height
Volume of Cube
A cube is a solid geometrical object with 6 faces.
All the sides of the cube are equal in length.
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Volume of the cube(V) = length × breadth × height
Volume of the cube(V) = s × s × s (where s is the side of the cube)
Volume of the cube(V) = s3
Volume by Counting Unit Cubes
We know that Volume is defined as a space occupied by a three-dimensional figure.
Let’s understand the concept of counting unit cubes with the help of the following examples:
Example: Find the volume of the given figure. Take the volume of each small cube as 1cm3.
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Solution
Step 1: We have to number the cubes.
A total of 6 cubes are present in the given figure.
So, cubes are numbered from 1 to 6.
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Step 2: Calculate the number of layers in the given figure.
A total of 2 layers are present in the given figure.
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Step3: Calculate the volume of each layer
Volume of layer= (Number of cubes in the layer × volume of small cube)
Volume of layer 1 = 3 × 1cm3 = 3 cm3
Volume of layer 2 = 3 × 1cm3 = 3 cm3
Step4 : Calculate the Total volume
Total volume= Volume of layer 1 + Volume of layer 2
So, Total Volume of figure = 3 cm3 + 3 cm3
Total Volume of figure = 6 cm3.
Solved Questions
1. Find the volume of the given figure. Take the volume of each small cube as 1cm3.
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Ans: Layer 1 contains 6 cubes,
So, Volume of layer 1 = 6 × 1cm3 = 6 cm3
Layer 2 contains 6 cubes,
So, Volume of layer 2 = 6 × 1cm3 = 6 cm3
Layer 3 contains 12 cubes, (6 in front + 6 in back)
So, Volume of layer 3 = 12 × 1cm3 = 12 cm3
So, Total Volume of figure = 6 cm3+6 cm3+12 cm3
Total Volume of figure = 24 cm3.
2. Find the volume of the cube having side 3 cm.
Ans: Volume of cube(V) = s3
Volume of cube(V) = (3)3
Volume of cube(V) = 3 cm × 3 cm × 3 cm
Volume of cube(V) = 27 cm3
3.Find the volume of the cuboid having l = 6 cm, b = 4 cm and h = 5 cm.
Ans: Volume of cuboid(V) = length × breadth × height
Volume of cuboid(V) = 6 cm × 4 cm × 5 cm
Volume of cuboid(V) = 120 cm3.
4. What is the volume of the pictures given below. Take the volume of each small cube as 1cm3.
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Ans: For figure A:
There is a total of 5 cubes
So, the Volume of figure A = 5 × 1cm3 = 5 cm3
For figure B:
There are a total of 12 cubes
(6 cubes in layer 1+ 6 cubes in layer 2)
So, Volume of figure B = 12 × 1cm3 = 12 cm3
Fun Facts:
When you link two points with only a line segment, you get a one-dimensional object that can only be measured in length.
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Two-dimensional figures are flat and have two dimensions i.e length and width. The area of a two-dimensional figure can be calculated by using length and width.
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The objects we come across on a daily basis are solid, three-dimensional objects with the following dimensions: length, width, and depth. The volume for three-dimensional objects is used to estimate their size.
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Summary
In this article we have discussed the concept of volume. First, we discussed volume definition, the volume of cube and cuboid concept and formulas, fun facts, and finally solved the problems. We have learned how to find the volume of figures by counting the unit cubes.
Learning by Doing
1. Jerry was flying a kite that was yellow in shade. Suddenly, a powerful wind blew, and his kite became tangled in a huge tree. Jerry-built a ladder made of cubical boxes. Now let us count the volume of the ladder to help Jerry in getting his yellow kite. Take the volume of each small cube as 1cm3.
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2. Tim wants to pack his old books in the cubical box. Help Tim in finding the volume of the cubical box on the side 5 cm.
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3. Miss Mary went shopping and bought too many clothes. Now, Miss Mary wants to place all her clothes in her cuboidal cupboard. Let's help Miss Mary in finding the volume of the cuboidal cupboard whose l = 4 cm, b = 3 cm, and h = 6 cm.
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FAQs on Volume of Geometrical Figures Explained Clearly
1. What is volume in geometry?
The volume of a geometrical figure is the amount of three-dimensional space it occupies. It is measured in cubic units such as cm³, m³, or in³. Volume applies only to 3D shapes like cubes, cylinders, cones, and spheres. For example, a box that is 2 cm long, 3 cm wide, and 4 cm high has a volume of 24 cm³.
2. What is the formula for the volume of a cube?
The formula for the volume of a cube is V = a³, where a is the length of one side. Since all edges of a cube are equal, you multiply the side length three times.
- Example: If side = 5 cm
- V = 5 × 5 × 5 = 125 cm³
3. How do you calculate the volume of a cuboid?
The volume of a cuboid is calculated using V = l × b × h, where l = length, b = breadth, and h = height. Multiply the three dimensions to get the volume.
- Example: l = 6 cm, b = 4 cm, h = 3 cm
- V = 6 × 4 × 3 = 72 cm³
4. What is the formula for the volume of a cylinder?
The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height. It is found by multiplying the area of the circular base by the height.
- Example: r = 3 cm, h = 7 cm
- V = π × 3² × 7 = 63π ≈ 197.92 cm³
5. What is the formula for the volume of a sphere?
The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius. It calculates the space enclosed inside a perfectly round 3D object.
- Example: r = 3 cm
- V = (4/3)π × 27 = 36π ≈ 113.10 cm³
6. How do you find the volume of a cone?
The volume of a cone is given by V = (1/3)πr²h, where r is the base radius and h is the height. It is one-third the volume of a cylinder with the same base and height.
- Example: r = 4 cm, h = 9 cm
- V = (1/3)π × 16 × 9 = 48π ≈ 150.72 cm³
7. What is the difference between area and volume?
The key difference is that area measures two-dimensional space while volume measures three-dimensional space.
- Area is measured in square units (cm², m²).
- Volume is measured in cubic units (cm³, m³).
- Area applies to flat shapes like squares and circles.
- Volume applies to solids like cubes and spheres.
8. What are the units of volume in geometry?
Volume is measured in cubic units such as cm³, m³, mm³, and in³. The unit depends on the unit of length used in the dimensions.
- If dimensions are in cm → volume is in cm³.
- If dimensions are in m → volume is in m³.
9. How do you solve volume word problems step by step?
To solve volume word problems, first identify the shape and then apply the correct volume formula. Follow these steps:
- Identify the 3D shape (cube, cylinder, sphere, etc.).
- Write the correct volume formula.
- Substitute the given values carefully.
- Calculate and write the answer in cubic units.
10. Why is volume important in real life?
Volume is important because it helps measure the capacity or space inside real-life objects. It is used in:
- Calculating storage capacity of tanks and containers.
- Measuring liquids in liters and cubic meters.
- Construction and engineering projects.
- Packaging and shipping industries.
