Volume Formulas for Different Geometrical Shapes

Niharika Arya Apr 28, 2019
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Volume formula depends upon the area of an object, but as the area changes according to the shape, the volume changes as well. Let's find out formulas for calculating volume of different shapes and size.
Volume is a space occupied by a three dimensional object. The object can be of any shape like square, triangle, rectangle, sphere, cylindrical, etc. Volume formula depends upon the area of the object. As the area of the object changes with the change in shape, the volume of the object also changes.
So there are different volume formulas for different shapes and sizes. The SI unit for volume is cubic meter (m3). For smaller measurements liter is used as the unit for measuring volume, where 1000 liters is equal to 1 cubic meter.
Volume can also be called capacity. Capacity means the amount of fluid that can be filled in the container or which the container can hold. There are few point which differentiate volume and capacity.
In acoustics, volume is a synonym of loudness or the level of sound. Well may be it has many meanings but we are here to discuss how to calculate volume of different shaped objects.

Different Volume Formulas

As we all know that there are different volume formulas for different shapes let's check few of them.

Cylinder

A cylinder is a solid which has 2 parallel faces that are actually 2 congruent circles.
These circles can also be called two bases of the cylinder. It has curved surface which connects these two surfaces and the perpendicular distance between the two circles is the height of the cylinder.
The formula for calculating volume of a cylinder is:

Volume = Area of Base × Height
V = π r2 h (Here r is radius of the cylinder and h is the height or the length of the cylinder)
You can also calculate the volume of a hollow cylinder tube. In this you have two radius. One is of the inner surface and the other is of the outer surface. So the formula will be:

V = π h (R2 - r2) (Here R is the radius of the outer surface and r is the radius of the inner surface)

Prism

A prism is a triangular solid which has two congruent polygonal faces. These faces form the 2 base of the prism.
Prism can be in a square or a rectangular form also. In such cases it has lateral faces. So volume formula for a triangular prism is:
Volume = Area of Base × Length
V = A l (Here A is the area of the prim and l is the length of the prism)

Cone

A solid cone has a circular base and a pointed tip. It has a curved surface which decreases in size as it goes to the vertex. The perpendicular distance from the base to the vertex is considered as the height of the prism. So the formula for volume of a cone will be:
Volume = ⅓ × Area of Base × Height
V = ⅓ π r2 h (Here r is the radius of the base and h is the height of the cone)

Pyramid

A pyramid is a solid with one polygonal base. It may have many triangular lateral faces which meets at a common point or vertex. We can find pyramids of different shapes of bases like rectangular pyramids, triangular pyramids etc. The perpendicular distance from the base to the vertex is considered as the height of the pyramid. So, the formula will be:
Volume = ⅓ × Area of Base × Height
V = ⅓ l w h (Here l is the length of the base, w is width of base, and h is the height of the pyramid)

Cube

A cube is a rectangular solid. All the edges of a cube are equal i.e. length = height = width. So the formula will be:
Volume = Length × Height × Width
V = L × H × W 
OR
V = a3 (Here a is length of any side)

Sphere

A sphere is a solid 3 dimensional circular object. All the points on the surface of the sphere are equidistant from the center of it.
The radius of the sphere is the distance form the center to the surface of the sphere. So, the volume of a sphere will be:

Volume = 4/3 π r3 (Where r is the radius of the sphere)
You can also find out the volume of the hemisphere. Hemisphere is a half sphere which has one base and a dome shaped face.

Volume = 1/2 (4/3 π r3) = 2/3 π r3 (Where r is the radius of a hemisphere)
Hope the formulas given here will help you to solve many mathematical problems. So, just take out your note book and start practicing now.