Question

The volume of the cube is 1.331 \[c{m^3}\]. Find the length of its edge. If the length of the edge is doubled, by how many times will the volume increase?

Answer 1

Hint: A cube is a three-dimensional solid object bounded by six square faces or sides, with three meeting at each vertex. It has 6 faces, 12 edges and 8 vertices.
Volume of cube of edge/side (a) =\[{a^3}\].

Complete step-by-step answer:

Given volume of cube=1.331\[c{m^3}\]
\[
   \Rightarrow {a^3} = 1.331 \\
   \Rightarrow {a^3} = \dfrac{{1331}}{{1000}} \\
   \Rightarrow a = \sqrt[{\dfrac{1}{3}}]{{\dfrac{{1331}}{{1000}}}} \\
   \Rightarrow a = \dfrac{{11}}{{10}} = 1.1cm \\
\]
Required side of the cube=1.1 cm
We know that, volume of cube of edge/side (a) =\[{a^3}\]
When side gets doubles i.e. side equals 2a, then the volume \[ \Rightarrow {(2a)^3} = 8{a^3}\]
The volume will become eight times when the side / edge of the cube is doubled.

Note: If the side/edge of a cube becomes x times the original one,
 then the new volume will always be \[{x^3}\] times the older one.
\[New{\text{ }}volume:{(x)^3} \times (The{\text{ }}original{\text{ }}volume)\]