Question

The volume of a sphere is $1.76c{m^3}$. The volume of 25 such spheres taking into account the significant figure is:
(A) $0.44 \times {10^2}\,c{m^3}$
(B) $44.00\,c{m^3}$
(C) $44.0\,c{m^3}$
(D) $44\,c{m^3}$

Answer 1

Hint:The given question is very simple. The volume of 25 spheres will be given by the product of the volume of 1 sphere with 25. The answer will have the exact same number of the significant digits as the volume of 1 sphere that is given in the question has.

Complete step by step answer:
The diagram representing a sphere is as follows:

Let us understand the given statement first.
It’s given that, “The volume of 25 such spheres taken into account.” Thus, the statement means that 25 spheres have the same volume as that of the volume of a sphere given. So the answer for the volume of the 25 spheres will be the volume of one sphere multiplied with 25.
Thus, from the question we have the volume of a sphere equal to $1.76c{m^3}$.
$ \Rightarrow V = 1.76\,c{m^3}$
Therefore, the volume of 25 such spheres is given as,
$ V = 25 \times 1.76\,c{m^3} \\
   \Rightarrow V = 44c{m^3} $
The question has an additional statement regarding the significant figure.
The significant figure refers to the number of digits present in the number. In this case, the volume of a sphere is represented using 3 digits, that is, 1.76. Thus, the answer for the volume of 25 such spheres should also be represented using 3 digits.
As the result we have obtained is 44, thus, we will place a decimal point and after that a zero, such that, the value of this result does not get changed.
So, the final result is $44.0\,c{m^3}$.
$\therefore $ As the volume of such spheres is $44.0\,c{m^3}$, thus, option (C) is correct.

Note:
The significant figures in a number are the digits that carry a meaningful contribution to its measurement resolution. In a number the digits with the highest exponent value is the most significant figure, whereas the one with the lowest exponent value is the least significant figure.