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 = a^{3} | |
2 | Rectangular Prism | Volume = `aXbXc` | |
3 | Cone | Volume = `1/3 pi r2 h` | |
4 | Cylinder | Volume = ^{`pi`} r^{2} h | |
5 | Pyramid | Volume = `1/3` b^{2}`h` | |
6 | Sphere | Volume = `4/3 pi` r^{3} | |
7 | Regular square prism | Volume = S^{2}h | |
8 | regular hexagonal prism | Volume = 3ash | |
9 | regular square pyramid | Volume = `1/3` b^{2}h | |
10 | regular pentagonal pyramid | Volume = `1/6`anbh
n= no.of sides |
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.
Solution:-
Given side measure of cube is 5 centimeter.
The formula used to find the volume of cube is a^{3}
a– side measure of the cube.
Volume = a^{3}
We know a = 5.
Plugging it in to the formula. We get,
Volume = 5^{3}.
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,
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
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` r^{2}h.
Here as given the value of r = 5, h =10
Volume = `pi` r^{2}h.
By plugging in the given values in to the given formula
Volume = `pi` 5^{2} 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 ?
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 ?
Answer:- 60 cubic centimeter.
I like to share this neet exam pattern with you all through my article.
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