Question

2 boxes cube with edges a=38cm and b=81cm is to be replaced by one cube shaped box of the same overall volume. How long will be its edge?

Answer 1

Answer:

A cube is a solid box whose every surface is a square of same area.

Take an empty box with open top in the shape of a cube whose each edge is 2 cm. Now fit cubes of edges 1 cm in it. From the figure it is clear that 8 such cubes will fit in it. So the volume of the box will be equal to the volume of 8 unit cubes together.

Therefore, the volume of the cube = 8 cu cm

Note that 8 = 2 × 2 × 2

Thus, volume of a cube = side × side × side = side3

Hence, a cube has:

(i) six surfaces or faces,

(ii) 8 vertices,

(iii) 12 edges or sides of equal length.

Cube

Since a cube has all sides equal.

Volume of a cube = (side × side × side) cubic units.

= 1 × 1 × 1 cubic units

Since area = side × side

Volume of a cube = (area × side) cubic units.

Answer 2

Answer:

83.697 cm

Step-by-step explanation:

Let the edge be x.

Then

x = 3√{ (38)^3 + (81)^3 = 83.697

Hence,

edge = x = 83.697 cm