Volume Formulas For 3d Shapes

 Introduction :-

Three-dimensional space is a geometric model of the physical universe in which we live. The three dimensions are commonly called length, width, and depth (or height) although any three mutually perpendicular directions can serve as the 3D. In this article we shall see about some 3D shapes and how to calculate their volume. The table below lists the formulae to calculate the volume of some common three dimensional shapes

Serial no. Name of the 3D shape Volume formula Diagram
1 Cube Volume  = a3 cube
2 Rectangular Prism Volume = `aXbXc` cuboid
3 Cone Volume = `1/3 pi r2 h` cone
4 Cylinder Volume = `pi` r2 h cylinder
5 Pyramid Volume = `1/3` b2`h` Pyramid
6 Sphere Volume = `4/3 pi` r3 sphere
7 Regular square prism Volume = S2h square prism
8 regular hexagonal prism Volume =  3ash Regular hexagonal prism
9 regular square pyramid Volume = `1/3` b2h square pyramid
10 regular pentagonal pyramid Volume = `1/6`anbh

n= no.of sides

pentagonal pyramid

 

I am planning to write more post on Constructing Parallel Lines and its example and, Rules for Exponents and its problem with solution. Keep checking my blog.

 

Solved Problems Based on Volume of three 3D shapes.

 

Problem :-1

Find the volume of cube which has the side measure of 5 centimeter.

cube 1

Solution:-

Given side measure of cube is 5 centimeter.

The formula used to find the volume of cube is a3

a– side measure of the cube.

Volume = a3

We know a = 5.

Plugging it in to the formula. We get,

Volume = 53.

53 = 5 * 5* 5 = 125.

So the volume of the given 3D shape is 125 cubic centimeter.

Problem 2

Find the volume of the 3D given below,

cuboid 1

With a = 5, b= 4 and c= 10.

Solution:-

By looking at the3D shape we can say that it is a rectangular prism.

The formula that is used to find the volume of rectangular prism is a*b*c.

Here as given the value of a = 5, b= 4, and c =10

Volume = a*b*c.

By plugging in the given values in to the given formula

Volume = 5 * 4* 10

By simplifying  we get the result as

Volume = 200.

The volume of the given 3D shape is 200 cubic centimeter.

Problem 3

Find the volume of the given 3D shape

With r = 5 and h = 10

cylinder 1

Solution:-

By looking at the3D shape we can say that it is a cylinder.

The formula that is used to find the volume of rectangular prism is `pi` r2h.

Here as given the value of r = 5, h =10

Volume =  `pi` r2h.

By plugging in the given values in to the given formula

Volume = `pi` 52 10

By simplifying the given values we get the result as
Volume = 250 `pi.`

The volume of the given 3D shape is 250` pi` cubic centimeter.

 

Solved Problems Based on Volume of three 3D shapes

 

Problem 1:-

Find the volume of the given 3D shape which has the measure of a  b =4 cm and h= 6cm ?

square pyramid 1

Answer:- 32 cubic centimeter.

Problem 2:-

Find the volume of the given 3D shape which has the measure of a  b =4 cm, a= 3cmand h= 6cm ?

pentagonal pyramid 1

Answer:- 60 cubic centimeter.

I like to share this neet exam pattern with you all through my article.

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