Question

A powder tin has a square base with side 8 cm and height 14 cm. Another tin has a
circular base with diameter 8 cm and height 14 cm. Find the difference in their capacities.

Answer 1

Hint: In this problem, first we have to calculate the volume of the square and the cylinder. Since the side lengths and the height of the square are given, we have to calculate the volume of the
square. Similarly, we have to calculate the volume of the cylinder for the given diameter and the
height. After that we have to subtract their volumes to get the difference.
The maximum capacity of a container is represented by the volume of the container.
Given that the square base with side = 8 cm
Height of the square = 14 cm
It is known that the volume of a rectangular cube $ = lbh$ , where $l$ is the length, $b$ is the
base and $h$ is the height.
Here the length and the base are equal which is 8 cm.
Now, substituting 8 for $l$, 8 for $b$, 14 for $h$.

Thus, Capacity
 $\begin{array}{c} = lbh\\ = 8 \times 8 \times 14\\ =
896\;{\rm{c}}{{\rm{m}}^3}\end{array}$

Similarly, diameter of the cylinder = 8 cm
Height of the cylinder = 14 cm
Converting diameter to the radius.
Radius of the cylinder $ = \dfrac{8}{2}$
= 4 cm
We know that the volume of a cylinder is represented by $\pi {r^2}h$, where $r$ is the radius of
the cylinder and $h$ is the height of the cylinder.
Substituting the value of 4 for $r$ and 14 for $h$.
Capacity of the cylinder
 $\begin{array}{c} = \pi {r^2}h\\ = \dfrac{{22}}{7} \times {4^2} \times
14\\ = \dfrac{{22}}{7} \times 16 \times 14\\ = 704\;{\rm{c}}{{\rm{m}}^3}\end{array}$

Now, subtracting the capacity of the cylinder from the capacity of the square based volume.
Difference in capacities
 $\begin{array}{c} = 896 - 704\\ =
192\;{\rm{c}}{{\rm{m}}^3}\end{array}$

Hence, the required volume is $192\;{\rm{c}}{{\rm{m}}^3}$
Note: Make sure to write the appropriate unit associated with the volume of the specific quantities.Also, after finding out the volumes of the circular and square based tins, REMEMBER to find the difference between the two to find the required answer