Measuring the volumes of solids is done using the volume formulas for the different solids. Volume of a solid is defined as the space occupied by the solid and is calculated using various formulas.
In this article, we will explore the measuring of solids in depth along with the basic information of volumes. We will also solve some examples related to measuring the volume of solids. Let’s start our learning on the topic “Measuring Volume of Solids”.
Measuring Volume of Different Solids
Below we will discuss the volumes of different solids.
Volume of Cube
Cube is a 3-D figure with 6 square faces, 8 vertices and 12 edges. All sides of the cube are equal.
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The volume of the cube is given by:
Volume of Cube = a3
a is the side of a cube
Volume of Cuboid
Cuboid is a 3-D figure with 6 rectangular faces, 8 vertices and 12 edges. The cuboid has three dimensions length, breadth and height.
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The volume of the cuboid is given by:
Volume of Cuboid = l.b.h
where,
- l is length of cuboid
- b is breadth of cuboid
- h is height of cuboid
Volume of Cylinder
Cylinder is the 3-D figure with rectangular curved side which is perpendicular to the two circular bases. The two circular base of cylinder are parallel to each other. The cylinder have two dimensions radius of the base and height.
The volume of the cylinder is given by:
Volume of Cylinder = πr2h
where,
- h is height of cylinder
- r is radius of cylinder
Volume of Cone
Cone is the 3-D figure made up of curved triangular side and a circular base. The cone has three dimensions height of cone, slant height and radius of the base.
The volume of the cone is given by:
Volume of Cone = (1/3) πr2h
where,
- h is height of cone
- r is radius of cone
Volume of Sphere
Sphere is the 3-D figure of 2-D circle. It does not have any vertex. It has a dimension i.e., radius of the sphere.
The volume of the sphere is given by:
Volume of Sphere = (4/3) π r3
where,
- r is the radius of sphere
Volume of Hemisphere
Hemisphere is the 3-D figure of 2-D semicircle. It has a dimensions i.e., radius of hemisphere.
The volume of the hemisphere is given by:
Volume of Hemisphere = (2/3) π r3
where,
- r is the radius of hemisphere
Volume of Triangular Prism
Triangular prism is a 3-D figure with three rectangular faces and two triangular base. The triangular bases are parallel to each other and the rectangular faces are perpendicular to the triangular faces.
The volume of the prism is given by:
Volume of Triangular Prism = Area of Base × Height of Prism
Volume of Pyramid
Pyramid is a 3-D figure with a polygon base and triangular faces that meet at same vertex. The volume of the pyramid is given by:
Volume of Pyramid = (1/3) × Area of Base × Height
Volume of Composite Solids
The volume of composite solids is determined by the sum of volumes of all the solids present in the composite figure.
Volume of Composite Solids = Sum of Volumes of All Solids in Composite Figure
Volumes of different solids are given in the table added below:
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Examples on Measuring Volumes of Solids
Example 1: Find the volume of cube with side 5 units.
Solution:
Volume of cube is given by:
Volume of Cube = a3
= 53
Volume of Cube = 125 cubic units.
Example 2: Find the volume of the cuboid with its length, breadth, height is 12 units, 10 units and 8 units respectively.
Solution:
Volume of cuboid is given by:
Volume of Cuboid = l.b.h
= 12 × 10 × 8
Volume of Cuboid = 960 cubic units.
Example 3: Find the volume of the cone with height 10 units and radius 4 units.
Solution:
Volume of cone is given by:
Volume of Cone = (1/3) πr2h
= (1/3) π42 × 10
= (1/3) π× 16 × 10
Volume of Cone = 167.55 cubic units
Example 4: Find the volume of cylinder with height 15 units and radius 2 units.
Solution:
Volume of cylinder is given by:
Volume of Cylinder = πr2h
= π22 (15)
= π × 4 × 15
Volume of Cylinder = 60Ï€ cubic units
Example 5: Find the volume of sphere with radius 7 units.
Solution:
Volume of sphere is given by:
Volume of Sphere = (4/3) π r3
= (4/3) π 73
= (4/3) π × 343
Volume of Sphere = 1436.75 cubic units
Example 6: Find the volume of hemisphere with radius 3 units.
Solution:
Volume of hemisphere is given by:
Volume of Hemisphere = (2/3) π r3
= (2/3) π 33
= 2π × 9
Volume of Hemisphere = 18Ï€ cubic units
Example 7: Find the volume of triangular prism with the area of base 12 sq. units and height of prism is 12 units.
Solution:
Volume of triangular prism is given by:
Volume of Triangular Prism = Area of Base × Height of Prism
= 12 × 12
Volume of Triangular Prism = 144 cubic units
Example 8: Find the volume of composite solid made up of two solids cylinder and cone. The volume of cylinder is 30 cubic units and volume of cone is 22 cubic units.
Solution:
Volume of composite solid is given by:
Volume of Composite Solid = Sum of Volumes of Solids Involved
Here,
Volume of Composite Solid = Volume of Cylinder + Volume of Cone
= 30 + 22
Volume of Composite Solid = 52 cubic units
Practice Questions on Measuring Volume of Solids
Q1. Find the volume of cube with side 18 units.
Q2. Find the volume of the cuboid with its length, breadth, height is 24 units, 17 units and 9 units respectively.
Q3. Find the volume of the cone with height 20 units and radius 14 units.
Q4. Find the volume of cylinder with height 19 units and radius 17 units.
Q5. Find the volume of sphere with radius 13 units.
Q6. Find the volume of hemisphere with radius 11 units.
Q7. Find the volume of prism with the area of base 26 sq. units and height of prism is 15 units.
FAQs on Volumes of Solids
What is the Volume of Solids?
Volume of solids is defined as the capacity of the solid.
What is the Volume Unit of Solids?
Volume units of solids is cubic units.
What is the Basic Volume Formula?
Basic volume formula is length × breadth × height.
How to Calculate Volumes of Solids?
To calculate the volumes of different solids we use the different volu.e formulas.
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