 QUESTION

# The volume of a cube is $1000c{{m}^{2}}$. Find its total surface area.

Hint: Form the volume of a cube, find the side of a cube. Substitute the value of the side in the formula for total surface area of the cube.

We have been given the volume of cube $=1000c{{m}^{2}}$
We know that the volume of the cube $={{\left( side \right)}^{3}}$.
Thus volume of the cube $={{\left( side \right)}^{3}}=1000c{{m}^{3}}$.
$\therefore {{\left( side \right)}^{3}}=1000c{{m}^{3}}$.
Now let us take the side of the cube as a.
$\therefore {{a}^{3}}=1000$
Now let us take cube root on both sides, we get,
$a=\sqrt{1000}=\sqrt{10\times 10\times 10}=\sqrt{{{10}^{3}}}=10$
Hence, the side of the cube = a = 10 cm.
We know that a cube consists of 6 sides, i.e. 6 square faces.
We know that the area of a square of side a = ${{a}^{2}}$.
Thus the total surface area of cube $=6\times$area of each side $=6\times {{\left( side \right)}^{2}}=6\times {{a}^{2}}=6{{a}^{2}}c{{m}^{2}}$.
Hence, total surface area of the cube = $6{{a}^{2}}c{{m}^{2}}$.
Put a = 10 cm.
Hence, the total surface area of the cube = $6\times {{10}^{2}}=6\times 10\times 10=6\times 100=600c{{m}^{2}}$.
Thus we got the total surface area of the cube as $600c{{m}^{2}}$.

Note: The sum of the area of all external surfaces of a three dimensional object is the TSA (total surface area). So either remember the formula to calculate TSA of a cube or you should know how to form the formula of TSA. Measurement of surface area is very important to use if we are concerned with quantities of material.