FIND VOLUME OF CUBE GIVEN SURFACE AREA

In Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.

Volume of cube = a³

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

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.

6a² = surface area of the cube

Surface area of new cube = 6(0.70a)²

= 2.94 a²

2.94a² = 1176

a² = 1176/2.94

a² = 400

a = √400

a = 20

So, side length 20 cm.

So, the volume of cube V = 8000 cm³