Question

The total volume of the cube is $1000c{{m}^{3}}$ . Find its total surface area in $c{{m}^{2}}$ .

Answer 1

Hint: Focus on the point that the volume of a cube is equal to the cube of the length of its side, and the surface area of a cube is 6 times the square of the length of its side.

Complete step-by-step answer:
Let us start by drawing a representative figure for better visualisation.

To start with the solution, we let the length of each side of the cube to be a cm.
As given in the question, the volume of the cube is 1000 $c{{m}^{3}}$ , and we know that the volume of a cube is equal to the cube of the length of its sides and all its sides are equal. Using this we can say that:
The volume of cube = ${{\left( \text{length of side} \right)}^{3}}$
$\Rightarrow 1000={{a}^{3}}$
$\Rightarrow a=\sqrt[3]{1000}=10\text{ cm}$
Now according to the question, we need to find the total surface area of the given cube. We know that the total surface area of a cube is 6 times the square of the length of its side.
$\therefore $ The total surface area of cube = $6{{\left( \text{length of side} \right)}^{2}}=6{{a}^{2}}=6\times 100=600\text{ c}{{\text{m}}^{2}}$
Therefore, the answer to the above question is $600\text{ c}{{\text{m}}^{2}}$ .

Note: Make sure to convert all the dimensions to a standardized system of units, this decreases the chance of errors. It would also help if we remembered all the basic formulas for surface area and volume of the general 3-D shapes like the cone, cube, cylinder, etc.