Question

A cubic foot of water is poured into a rectangular aquarium with base 15 inch by 18 inch. To what height in inches does the water rise.
(a) $6{\displaystyle \frac{2}{5}}$
(b) 6
(c) $5{\displaystyle \frac{3}{4}}$
(d) $5{\displaystyle \frac{1}{2}}$
(e) 5

Answer 1

Hint: First, the condition given in the question is that the aquarium is $1f{t}^3$ in volume and we need to convert the volume of the aquarium into units of inches. Then, we also know the formula to calculate the volume of the aquarium which is actually a cuboid as $V=l\times b\times h$ . Then, substituting the value of l, b and equating it with the above volume, we get the height of the aquarium.

Complete step-by-step answer:
In this question, we are supposed to find the height of the rectangular aquarium which is actually a cuboid of length 18 inch, breadth 15 inch and height as h.
So, the figure to show these dimensions is as:

Now, the condition given in the question is that the aquarium is $1f{t}^3$ in volume.
But, all the dimensions are given in inches, so we need to convert the volume of the aquarium into units of inches.
Then, we know by the relation as:
 $1ft=12in.$
So, the volume(V) of the aquarium inch inches comes out to be:
 $\begin{array}{rl}& V={(12in.)}^3\\ & \Rightarrow V=1728in{.}^3\end{array}$
Now, we also know the formula to calculate the volume of aquarium which is actually a cuboid as:
 $V=l\times b\times h$
So, by substituting the value of l, b and equating it with the above volume, we get:
 $\begin{array}{rl}& l\times b\times h=1728\\ & \Rightarrow 18\times 15\times h=1728\end{array}$
So, by solving the above equation, we can get the height to which water rises as:
 $\begin{array}{rl}& h={\displaystyle \frac{1728}{18\times 15}}\\ & \Rightarrow h={\displaystyle \frac{1728}{270}}\\ & \Rightarrow h={\displaystyle \frac{32}{5}}\\ & \Rightarrow h=6{\displaystyle \frac{2}{5}}\end{array}$
So, the height of the aquarium is $6{\displaystyle \frac{2}{5}}$ in.
Hence, option (a) is correct.

Note: In these type of questions, firstly we should know some of the conversions such that we are very comfortable in converting them to desired units as:
 $\begin{array}{rl}& 1ft=12in.\\ & 1km=1000m\\ & 1m=100cm\end{array}$
Secondly, we must know the basic formulas of the 3D figures as:
Volume of cuboid as $V=l\times b\times h$ .