Question

An Olympic swimming pool is in the shape of a cuboid of dimensions 50 m long and 25 m wide. If it is 3m deep throughout, how many litres of water does it hold?

Answer 1

Hint: We should know that the volume of a 3D figure is equal to the product area of base and height of 3D figure. So, the volume of cuboid is equal to product of area of base of cuboid and height of cuboid. Now we have to find the shape of the base of the cuboid, which we will get as a rectangle. Then we have to find the area of the base of the cuboid. As the height of the cuboid is given, we can find the volume of the cuboid. Now we have to convert the cubic metric units to litres.

Complete step-by-step answer:
Before solving the question, we should know that the volume of a 3D figure is equal to the product area of base and height of 3D figure.

Let us assume a cuboid whose length is equal to 50 m and breadth is equal to 25 m and depth is equal to 3 m.
We know that a cuboid is a 3D figure. We know that the volume of a 3D figure is equal to the product area of base and height of the 3D figure. So, the volume of cuboid is equal to area of base of cuboid and height of cuboid.
We know that the base of a cuboid is a rectangle. We know that if the length and breadth of a rectangle are a and b respectively, then the area of the rectangle is equal to product of a and b.
If the sides of the base of cuboid is equal to l and b where l is length of cuboid and b is breadth of cuboid, then the area of cuboid is equal to lb.
Let us assume the area of the cuboid is equal to A.
\[\Rightarrow A=lb\]
From the question, it was given that the length of the cuboid is equal to 50 m and the breadth of cuboid is equal to 25 m.
\[\begin{align}
  & \Rightarrow A=(50)(25) \\
 & \Rightarrow A=1250{{m}^{2}} \\
\end{align}\]
So, the area of the base of the cuboid is equal to \[1250{{m}^{2}}\].
We know that the height of cuboids is equal to 3m.
If the area of the base is equal to A and height is equal to h, then the volume of cuboid is equal to Ah.
Let us assume the volume of cuboid whose area is equal to 1250 and height is equal to 3 is equal to V.
\[\begin{align}
  & \Rightarrow V=Ah \\
 & \Rightarrow V=(1250)(3){{m}^{3}} \\
 & \Rightarrow V=6250{{m}^{3}} \\
\end{align}\]
So, the volume of cuboid is equal to \[6250{{m}^{3}}\].
We know that 1 metric cube is equal to 1000 litres.
\[\Rightarrow V=625\times {{10}^{4}}litres\]
So, the litres of water the cuboid holds equal to \[625\times {{10}^{4}}\].

Note: This problem can be solved in an alternative manner.
We know that the volume of cuboid whose length is l, breadth is b and height is h is equal to \[lbh\].
Let us assume the volume of cuboid whose length is equal to 50 m, breadth is equal to 25 m and height is equal to 3m is equal to V.
\[\begin{align}
  & \Rightarrow V=(50)(25)(3){{m}^{3}} \\
 & \Rightarrow V=6250{{m}^{3}} \\
\end{align}\]
So, the volume of cuboid is equal to \[6250{{m}^{3}}\].
We know that 1 metric cube is equal to 1000 litres.
\[\Rightarrow V=625\times {{10}^{4}}litres\]
So, the litres of water the cuboid holds equal to \[625\times {{10}^{4}}\].