Question

Given $f=c{{d}^{3}}$ where f=450 and d=10. Find the value of c?
(a) 0.45
(b) 4.5
(c) 15
(d) 45
(e) 150

Answer 1

Hint: First, by proceeding in the manner stated above we are given with the expression as $f=c{{d}^{3}}$where we are asked to find the value of c. Then, we will rearrange the given expression in the form we get the value of c as $c=\dfrac{f}{{{d}^{3}}}$. Then, by substituting the value of f and d which are given in the question as 450 and 10, we get the value of c.

Complete step by step answer:
In this question, we are supposed to find the value of c for the given expression as $f=c{{d}^{3}}$where f=450 and d=10.
So, before proceeding for this, we must know that the given problem is of basic substitution to get the third value when two of the values of the expression are already given.
Now, by proceeding in the manner stated above we are given with the expression as $f=c{{d}^{3}}$where we are asked to find the value of c.
So, we will rearrange the given expression in the form we get the value of c as:
$c=\dfrac{f}{{{d}^{3}}}$
Now, by substituting the value of f and d which are given in the question as 450 and 10, we get:
\[c=\dfrac{450}{{{10}^{3}}}\]
Then, by solving the above expression, we get the value of c as:
\[\begin{align}
  & c=\dfrac{450}{1000} \\
 & \Rightarrow c=0.45 \\
\end{align}\]
So, we get the value of c as 0.45.
Hence, option (a) is correct.

Note:
Now, to solve these types of questions we need to know some of the basics of the cube of the number beforehand so that questions can be solved easily. So, the cube of the number means multiplying the same number three times instead of multiplying it with three.