Question

The volume of a cube is \[1000c{{m}^{2}}\]. Find its total surface area.

Answer 1

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.

Complete step-by-step answer:
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,
\[a=\sqrt[3]{1000}=\sqrt[3]{10\times 10\times 10}=\sqrt[3]{{{10}^{3}}}=10\]
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.