Question

Find the length of the gift box, whose volume is $8000{\text{ }}{{\text{m}}^3}$.
$
  {\text{A}}{\text{. 12 m}} \\
  {\text{B}}{\text{. 18 m}} \\
  {\text{C}}{\text{. 20 m}} \\
  {\text{D}}{\text{. 10 m}} \\
 $

Answer 1

Hint:Cuboid is a three-dimensional mathematical body which has the same sides, i.e., length, width as well as the height of a cuboid is equal. The volume of an object is defined as the quantity of air/space enclosed by any three-dimensional body. Every defined and regular three-dimensional body has a predefined formula for the calculation of the volume.

Here, in this question, we have been given the volume of the gift box which is cuboid in shape, and we need to determine the length of the sides of the gift box for which we have to use the standard formula for the volume of the cuboid. The volume of the cuboid is $V = {a^3}$ where a is the length of the sides.


Complete step-by-step solution
In the question, it is not given about the shape of the gift box, but in general, the gift boxes are cuboid in shape which has length, width as well as the height equal in dimension.
Here, the volume of the gift box has been given as $8000{\text{ }}{{\text{m}}^3}$.

Also, the mathematical formula for the volume of the cuboid is $V = {a^3}$ where, $a$ is the dimension of the length, width and height of the gift box.
According to the question, $V = 8000{\text{ }}{{\text{m}}^3}$
Substitute $V = 8000{\text{ }}{{\text{m}}^3}$ in the formula of the volume of the cube as: $V = {a^3}$ to determine the length of the sides of the cube.
$
  V = 8000 \\
  {a^3} = 8000 \\
  {a^3} = {20^3} \\
  a = 20{\text{ m}} \\
 $
Hence, the length of the sides of the gift box whose volume is $8000{\text{ }}{{\text{m}}^3}$ is 20 meters.

Hence the correct answer is option C .

Note: Students often confuse the terms volume, surface area and the total surface area of the three-dimensional bodies. All these three terms are different and have different formulae. Surface area is the area of the rim of the three-dimensional body which can be seen with the naked eyes or can be touched