Volume of the shape means the capacity of the shape. To calculate volumes of different shapes we have different formulas. The basic formula for volume is obtained by multiplying length, breadth and height.
In this article, we will explore how to calculate volumes for different shapes. Also, we will solve some examples related to how to calculate volumes.
Volume Definition
Volume is the measure of the region covered by the 3-D solids. In other words, volume is defined as the capacity of a closed surface in three-dimensional space. The unit of volume is cubic units. The volume of various figures is used for various purposes. Volume formulas also have real-life applications, such as finding the volume of containers, the volume of the water tank, and others.
Formulas used to calculate the volume of various figures is shown in the image added below:
Volume of 3D-Shapes
Volume formulas of different solids are given below:
Volume of Cube
A cube is a 3-D shape in which all its dimensions are equal. (i.e. l = b =h). Rubik’s cube is a very common example of a cube. A cube of side ‘a’ is shown in the image below:
.png)
Volume of the cube formula is given by:
Volume of Cube = a3
where,
Volume of Cuboid
A cubiod is a 3-D shape in which all its dimensions are different or may be any two are equal. Matchbox is a very common example of cubiod. A cuboid of length ‘l’, breadth ‘b’, and height ‘h’ is shown in the image below:
.png)
Volume of cuboid formula is given by:
Volume of Cuboid = lbh
where,
- l, b, h are the length, breadth and height of cuboid
Volume of Cylinder
Cylinder is a 3-D which have two flat surfaces and a curved surface. Various example of cylinder are, water tankers, pipes, gas cylinders, etc. A cylinder of height ‘h’ and radius ‘r’ is shown in the image below:
Volume of cylinder formula is given by:
Volume of Cylinder = πr2h
where,
- r is radius of cylinder
- h is height of cylinder
Volume of Sphere
A sphere is a three-dimensional geometric object that is perfectly round in shape, much like a ball. It is defined as the set of all points in three-dimensional space that are equidistant from a fixed point called the center. A sphere of radius ‘r’ is shown in the image below:
Volume of sphere formula is given by:
Volume of Sphere = (4 /3)Ï€r3
where,
Volume of Hemisphere
A hemisphere is a three-dimensional geometric shape that is half of a sphere. It is formed by slicing a sphere into two equal parts along a plane passing through its center. A hemisphere of radius ‘r’ is shown in the image below:
Volume of hemisphere formula is given by:
Volume of Hemisphere = (2 /3)Ï€r3
where,
- r is radius of hemisphere.
Volume of Cone
A cone is a three-dimensional geometric shape that tapers smoothly from a flat, circular base to a single point called the apex or vertex. It resembles a party hat or an ice cream cone. A cone of height ‘h’ and radius ‘r’ is shown in the image below:
Volume of cone formula is given by:
Volume of Cone = (1/3)Ï€r2 h
where,
- r is radius of cone
- h is height of the cone
Volume of a Pyramid
Pyramid is a three-dimensional geometric shape wich has polygonal base and triangular faces that meet at a common point called the apex. A prramid of height ‘h’ is shown in the image added below:
Formula for the volume of a pyramid is given as follows,
Volume of Pyramid(V) = 1/3 × Base Area × Height
V = 1/3 A.H cubic units
where,
- V is Volume of Pyramid
- A is Base Area of Pyramid
- H is Height of a Pyramid
Volume formulas for various figure are added in the table below:
Units of Volume
Volume of any 3-d shape is the space occupied by that shape and is calculated in unit3. The standard unit to measure the side of any 3-d shape is ‘m’ and so the volume of any 3-d shape is calculated in m3. Other units in which voluemof 3-d shapes is calculated is added in the table below:
| Unit of Side |
Unit of Volume |
Metric Equivalent |
| Inch |
Cubic Inches (in3) |
1 cu.in = 16.387064 ml |
| Foot |
Cubic Feet (ft3) |
1 cu.ft = 28.316846592 l |
| cm |
Cubic centimeter (cm3) |
1 cubic centimeter = 1 ml |
Now some times we came across scenarios in which general unit of volume are used and to convert these general unit of volume to standard unit of volume one must go through the table added below:
| Unit |
Conversion |
| 1 Pint (pt) |
2 cups |
| 1 Quart (qt) |
2 pt |
| 1 Gallon (gal) |
3.78 liters |
| 1 liter |
1000 cubic centimeter = 1000 ml |
How to Calculate Volume?
To calculate volume of any 3-d shapes follow the steps added below:
Step 1: Firstly, identify the shape.
Step 2: Apply the volume formula of the identified shape. If it is a complex shape divide the same into smaller general shape and yhen apply the volume formula to each dhape.
Step 3: Simplify the result and add all the volume of smaller shapes if required. Resultant value gives the volume of the given shape.
Step 4: Use appropriate cubic uniut in the answer to give the exact volume of given shape.
Using these steps one can easily found the volumeof the cube as shown in the examples added below:
Related:
Examples on Volume
Example 1: Find the volume of cube with side 5 units.
Solution:
Volume of cube is given by:
Volume of Cube = a3
V = 53
Volume of Cube = 125 cubic units
Example 2: Find the volume of cuboid with length, breadth and height as 9, 6 and 5 respectively.
Solution:
Volume of cuboid is given by:
Volume of Cuboid = lbh
V = 9 × 6 × 5
Volume of Cuboid = 270 cubic units
Example 3: Find the volume of cylinder with height 10 units and radius 5 units.
Solution:
Volume of cylinder is given by:
Volume of Cylinder = πr2h
V = π(5)2 × 10
Volume of Cylinder = 250Ï€ cubic units
Example 4: Find the volume of cone with height and radius as 13 and 6 units respectively.
Solution:
Volume of cone is given by:
Volume of Cone = (1 /3)Ï€r2h
V = (1 /3)π 62 × 13
V = 12 × 13π
Volume of Cone = 156Ï€ cubic units
Example 5: Find the volume of sphere whose radius is 9 units.
Solution:
Volume of sphere is given by:
Volume of Sphere = (4 / 3)Ï€r3
V = (4 / 3)Ï€ 93
V = 4 × 243 × π
Volume of Sphere = 972Ï€ cubic units
Example 6: Find the volume of hemisphere whose radius is 6 units.
Solution:
Volume of hemisphere is given by:
Volume of Hemisphere = (2/3)Ï€r3
V = (2 / 3)Ï€ 63
V = 4 × 36π
Volume of Hemisphere = 144Ï€ cubic units
Practice Questions on Volume
Q1. Find the volume of cube with side 13 units.
Q2. Find the volume of cuboid with length, breadth and height as 19, 8 and 11 respectively.
Q3. Find the volume of cylinder with height 11 units and radius 7 units.
Q4. Find the volume of cone with height and radius as 15 and 12 units respectively.
Q5. Find the volume of sphere whose radius is 4 units.
Q6. Find the volume of hemisphere whose radius is 7 units.
FAQs on Volume
What is Volume?
Volume is the mathematical quantity which gives the capacity of closed figure in 3-D space.
Basic formula for volume is given by:
Volume = Length × Breadth × Height
What is Unit of Volume?
Volume is measured in cubic units.
What is the Difference Between Volume and Area?
Volume of any 3-d spahe is the total space occupied bt that shape. It is calculated only for 3-d shapes. On the other hand area is calculated both fo 2-d and 3-d shapes. It is the space occupied by boundary of any figure in 2-d and 3-d.
What is the Volume of a ball?
A ball is considered to a sphere and hence its volume is given by the formula, V = 4/3Ï€r3
How do you Find the Volume of a Tank?
A tank is generally in the shape of cuboid and its volume is calculated by the formula: V = l.b.h
How to Calculate the Volume of an Irregular Shape?
To find the volume of Irregular shape we first break that irregular shape into smaller shapes such that volume of each smaller shape is easily calculated and then all the volume calculated are added to find the volume of the given irregular shape.
Share your thoughts in the comments
Please Login to comment...