Question

There is a reservoir shaped like a square prism. If the area of its bases is $225sq.cm$, how many liters of water will it hold?
A. $3.375$
B. $3375$
C. $33.75$
D. $337.5$

Answer 1

Hint - To solve this problem, firstly we have to study the shape, dimensions and formulas used to calculate the required quantities of a prism. Then we will find its side dimensions as we have the area given, and then at the final step, we will be finding the volume of the given reservoir which will help us in approaching our solution.

Complete step by step answer:
In Geometry, various three- dimensional shapes are there, which are also known as solid shapes.
For example - cubes, cylinder, prism, sphere.
According to the question, we have a reservoir which is shaped like a square prism. Hence, here we will focus on the square prism which is a three-dimensional shape cuboid figure whose bases are in square shape. The sides and their opposite angles are congruent to each other.

Square prism formulas
1. Surface area of the square prism,$SA\, = 2{a^2} + \,4ah\,sq\,units$
2. Volume of a Square Prism,$V\, = {a^2}h\,\,cubic\,units$
The base of the prism is square and its area is $225sq.cm.$ (Given)
Now, Area of square= side $ \times $ side
                                       $ = \left( {sid{e^2}} \right)$
 $
  225 = sid{e^2} \\
  side = \sqrt {225} \\
  side\, = 15 \\
    \\
 $
Square prisms are having their faces as squares.
Area of base is$225$
 $
    \\
   \Rightarrow Area\,of\,square = {a^2} = 225 \\
$
Therefore, $a = 15$
Height=$15$
Now we have to calculate the quantity of water it can hold. Hence -
Volume of prism = Base area$ \times $ height
$ = 225 \times 15 = 3375\,c.c$
$\therefore \,\,volume = 3.375\,litres$ (As we know that $1\,c.c = {10^{ - 3}}litres$)
Hence, the correct answer is option A. 3.375

Note - So, by working on sides and volume of the square prism we have found the capacity of the reservoir. We have used calculation formulas of Surface area and volume of the prism to find the volume of the reservoir as we know that it will give us the amount of water stored in the reservoir.