Question

Find the volume of a cube of side $ 15cm $ ?
(A) $ 3375c{m^3} $
(B) $ 3350c{m^3} $
(C) $ 3450c{m^3} $
(D) $ 3120c{m^3} $

Answer 1

Hint: Here in this question we want to find the volume of a cube whose side is given to us as $ 15cm $ . To find the volume of a square, we have a standard formula $ Volume = {\left( {Side} \right)^3} $ . We know the value of the side of the cube as it is provided to us in the problem itself. We substitute the known values and determine the volume of the required cube using the formula.

Complete step-by-step answer:
A cube is a regular solid with six square faces. Cubes have eight vertices and twelve edges, all of the same length.

To determine the volume of a cube, we have the standard formula $ V = {\left( {Side} \right)^3} $ where V represents the volume of the cube. The side of a cube is the line segment which joins any two consecutive vertices of the cube. The side of a cube is often denoted as ‘S’ or ‘s’. The unit for the volume is cubic units. In the given question, we are given the length of the side of the cube in centimetres. So, we get the volume of the cube using the formula in the unit $ c{m^3} $ .
To find the volume of the cube, we use formula $ V = {\left( {Side} \right)^3} $ .
The side of the cube is given as $ 15cm $ .
By substituting the value of side of the cube, we get,
 $ V = {\left( {Side} \right)^3} $
 $ \Rightarrow V = {\left( {15cm} \right)^3} $
Cube of a number can be calculated by raising the number to the third power.
Now, we calculate the cube of $ 15 $ and simplify the expression further,
 $ \Rightarrow V = 15 \times 15 \times 15\,c{m^3} $
 $ \Rightarrow V = 3375c{m^3} $
Hence, the volume of a cube whose length is given to us as $ 15cm $ is $ 3375\,c{m^3} $ .
Hence, option (A) is correct.

Note: Generally the volume is the amount of space occupied by a three dimensional figure as measured in cubic units. The given question revolves around the concepts of mensuration. One must know the formulae for finding volumes of solids in order to solve such questions. Care must be taken while handling calculations so as to be sure of the final answer. We can also directly find the answer to the problem if we remember the cube of the side length.