Question

Volume of a cube whose edge measures 5.8 cm is:
(a) 165.12 cubic cm
(b) 155.1121 cubic cm
(c) 195.112 cubic cm
(d) 175.21 cubic cm

Answer 1

Hint: In the above problem, we are going to use the formula of volume of a cube which is equal to the cube of the length of an edge or mathematically we can say that power of the length of the edge is 3. We have asked to find the volume of a cube. So, we need the dimensions of a cube and the formula for the volume of the cube.

Complete step-by-step solution
Cube is another form of a cuboid. When the length, breadth, and height of the cuboid are equal then it becomes a cube. The below figure is the diagram of a cube:

Let us assume that the length, breadth, and height of the cube be “a”. Now, we are going to derive the formula for the volume of a cube:
$\text{Volume of cube}=\left( \text{area of base} \right)\times \left( \text{height of cube} \right)$
In the above figure, the base is BCHF so the area of the base is shown below.
Area of the base $=a\times a={{a}^{2}}$
Height of the cube $=a$
∴Volume of cube $={{a}^{2}}\times a={{a}^{3}}$
It is given in the question that the length of the edge is equal to 5.8 cm so substituting the length of the edge in the formula of volume of the cube we get,
Volume of cube is equal to:
$\begin{align}
  & {{\left( 5.8cm \right)}^{3}} \\
 & =5.8\times 5.8\times 5.8c{{m}^{3}} \\
 & =33.64\times 5.8c{{m}^{3}} \\
 & =195.112c{{m}^{3}} \\
\end{align}$
Hence, the volume of the cube is equal to 195.112 cubic cm.
Hence, the correct option is (c).

Note: Don’t forget to write the units of volume like in this problem, the unit is in cubic cm. Sometimes, the question gets a little twisted like the edge length of the cube is given in cm and you have asked volume in cubic m then, first of all, convert the units of edge length from cm into m then put the edge length in the formula of volume of a cube.