Question

How do you evaluate the formula $V = \dfrac{{Bh}}{3}$ for $B = 36i{n^2}$ and $h = 11in$ ?

Answer 1

Hint: The values which we gave $B$ and $h$ are multiplied in the formula of the function $V$ . So substitute those values in the formula and multiply them to evaluate the answer. But do care of the unit of $V$ . It can be found by the units of $B$ and $h$ by substituting them the same way as their numeric values.

Complete step by step answer:
We are asked to evaluate the formula $V = \dfrac{{Bh}}{3}$ . It has two variables which are $B$ and $h$ . By substituting the numeric values of $B$ and $h$ we can calculate the numeric value of the function $V$ . We have the value $B = 36i{n^2}$ which has the unit of square inches. Any value which has a unit in squares must represent an area of a two dimensional plane. The second value we have is $h = 11in$ which has the unit in inches. It represents length or breadth.
We can see $B$ and $h$ are multiplied together in the formula. The multiplication of area with length must give volume of a three dimensional object. So $V$ here must represent volume here. Now let us substitute the values of $B$ and $h$ in the formula,
$V = \dfrac{{Bh}}{3}$
Put $B = 36i{n^2}$ and $h = 11in$
$ \Rightarrow V = \dfrac{{36 \times 11}}{3}$
$ \Rightarrow V = \dfrac{{396}}{3}$
On evaluating,
$ \Rightarrow V = 132$
We found the numeric value of $V$ to be $132$ but the answer is incomplete without units because we know $V$ represents volume.
We know $B$ and $h$ have the units square inches and inch respectively and they are multiplied together in the formula of $V$ . So to find the unit of $V$ let us multiply the units of $B$ and $h$ ,
$
  V = B \times h \\
   \Rightarrow V = i{n^2} \times in \\
   \Rightarrow V = i{n^3} \\
 $

Hence the unit of $V$ is inch cube, so final answer would be $V = 132i{n^3}$.

Note: The formula which we have $V = \dfrac{{Bh}}{3}$ is actually the formula to find the volume of a pyramid or cone, where $h$ is the altitude of the cone or pyramid and $B$ is the area of the base of cone or pyramid. The base can be anything from a circle to a square or a rectangle, what matters is the concept of multiplication base and height to find volume.