In Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
Volume of cube = a^{3}
To find side length of cube from the diagonal, we use the formula
Side length = a√3
Problem 1 :
Calculate the volume of the cube if its surface is 150 cm².
Solution :
Let ‘a’ be the side of the cube.
Surface area of cube = 150 cm²
6a² = 150
a² = 25
a = 5
Volume of the cube = a³
= 5³
V = 125 cm³
Problem 2 :
The cube has a surface of 600 cm². What is its volume?
Solution :
Given, Surface area of cube = 6a²
Let side of cube = a cm
Surface area = 6 × (side)² 600 = 6 × a² 600/6 = a² a² = 100 a = 10 cm |
Volume of cube = a³ V = (10)³ V = 1000 cm³ |
Problem 3 :
We make a box in the shape of a cube with an edge of 12 cm. how many cm² of sheet metal do we need to create a box if we do not make the lid?
Solution :
Edge a = 12 cm
Surface area of cube = 5 × a²
= 5 × 12
S = 720 cm²
Problem 4 :
If we reduce the length of the cube edge by 30%, this reduced cube has an area of 1176 cm². Specify the edge length and volume of the original cube.
Solution :
Let a be the length of the original cube.
This side length is going to be reduced by 30%. So length of new cube will be 70% of the original cube.
6a^{2} = surface area of the cube
Surface area of new cube = 6(0.70a)^{2}
= 2.94 a^{2}
2.94a^{2} = 1176
a^{2} = 1176/2.94
a^{2} = 400
a = √400
a = 20
So, side length 20 cm.
So, the volume of cube V = 8000 cm³
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM