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VOOZH | about |
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VOOZH | about |
Volume is the amount of space occupied by a three-dimensional (3D) object. It is calculated using formulas based on the shape and its dimensions.
Below are the formulas for different solids.
👁 Volume-FormulasA cube is a 3-D figure with 6 square faces, 8 vertices, and 12 edges. All sides of the cube are equal.
The volume of the cube is given by:
Volume of Cube = a3
- where, a is the side of a cube
A cuboid is a 3-D figure with 6 rectangular faces, 8 vertices, and 12 edges. The cuboid has three dimensions: length, breadth, and height.
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
A cylinder is a three-dimensional solid with two equal and parallel circular bases joined by a curved surface. It is defined by its radius 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
A cone is a three-dimensional solid with a circular base and a curved surface that converges to a vertex. It is defined by its radius, height, and slant height.
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
A sphereis the 3-D figure of a 2-D circle. It does not have any vertex. It has a dimension, i.e., the 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
A hemisphere is a three-dimensional shape obtained from a semicircle, and it is defined by its radius.
The volume of the hemisphere is given by
Volume of Hemisphere = (2/3) π r3
- where, r is the radius of hemisphere
A triangular prism is a 3-D figure with three rectangular faces and two triangular bases. 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
A pyramid is a 3-D figure with a polygon base and triangular faces that meet at the same vertex. The volume of the pyramid is given by:
Volume of Pyramid = (1/3) × Area of Base × Height
Example 1: Find the volume of a cube with a side of 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, and height being 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 a 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 = 60π cubic units
Example 5: Find the volume of a sphere with a radius of 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 a hemisphere with a radius of 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 = 18π cubic units
Example 7: Find the volume of a triangular prism with the area of the base being 12 sq. units and the height of the prism being 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 a composite solid made up of two solids, a cylinder and a cone. The volume of the cylinder is 30 cubic units, and the volume of the 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
Q1. Find the volume of a cube with a side of 18 units.
Q2. Find the volume of the cuboid with its length, breadth, and height being 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 a cylinder with height 19 units and radius 17 units.
Q5. Find the volume of a sphere with a radius of 13 units.
Q6. Find the volume of a hemisphere with a radius of 11 units.
Q7. Find the volume of a prism with the area of the base 26 sq. units and the height of the prism 15 units.
