Question

Find the total surface area of cubes having the following sides –
(a) 3cm
(b) 5cm
(c) 5.5cm

Answer 1

Hint: To calculate the total surface area of a cube, use the formula $6{{a}^{2}}$, where ‘a’ denotes the length of the edge of the cube. Substitute the value of ‘a’ in the formula and simplify it to get the total surface area of the cube.

Complete step-by-step answer:
We have to calculate the total surface area of a cube whose edges are of different lengths.

We know that the total surface area of the cube is given by $6{{a}^{2}}$, where ‘a’ denotes

the length of the edge of the cube.

We will calculate the total surface area of the cube in each case.
(a) We know that the length of the edge of the cube is 3cm.
Substituting $a=3$ in the formula $6{{a}^{2}}$, total surface area of the cube $=6{{\left( 3
\right)}^{2}}=54c{{m}^{2}}$.
Hence, the total surface area of the cube is $54c{{m}^{2}}$ when the length of the edge is 3cm.
(b) We know that the length of the edge of the cube is 5cm.
Substituting $a=5$ in the formula $6{{a}^{2}}$, total surface area of the cube $=6{{\left( 5
\right)}^{2}}=150c{{m}^{2}}$.
Hence, the total surface area of the cube is $150c{{m}^{2}}$ when the length of the edge is
5cm.
(c) We know that the length of the edge of the cube is 5.5cm.
Substituting $a=5.5$ in the formula $6{{a}^{2}}$, total surface area of the cube $=6{{\left( 5.5
 \right)}^{2}}=181.5c{{m}^{2}}$.
Hence, the total surface area of the cube is $181.5c{{m}^{2}}$ when the length of the edge is
5.5cm.

Note: It’s necessary to keep the units in mind while calculating the total surface area of the cube. The length of the edge of the cube is given in centimetres. So, the total surface area will have units in square centimetres. One must remember that the total surface area is $6{{a}^{2}}$, not $4{{a}^{2}}$ as it is the sum of the area of all the faces of the cube.