Question

A women self-help group (DWACRA) is supplied with a rectangular solid (cuboid shape) of wax with dimensions 66 cm, 42 cm, 21 cm to prepare cylindrical candles each 4.2 cm. in diameter and 2.8 cm. of height. Find the number of candles.

Answer 1

Hint: We have to consider the fact that the Volume of the rectangular solid wax is the same as the total volume of cylindrical candles. The volume of Cuboid, say V is given as $v = lbh$, where l is the length, b is the breadth and h is the height. The volume of the cylinder, say V’ is given as $V' = \pi {r^2}h$, where r is the radius, and h is the height.

Complete step-by-step answer:
The volume of the rectangular cuboid of wax is $v = lbh$, where l is the length, b is the breadth and h is the height.
$
   \Rightarrow v = 66 \times 42 \times 21 \\
   \Rightarrow v = 58212c{m^3} \\
 $
Therefore, the volume of the solid wax is $58212c{m^3}$
Now, The volume of the cylindrical shape candles is, say V’ is given as $V' = \pi {r^2}h$, where r is the radius and h is the height.
In question, it is given that diameter is 4.2cm and height is 2.8cm.
Since we know $radius = \dfrac{{diameter}}{2} = \dfrac{{4.2}}{2} = 2.1cm$
$
   \Rightarrow v' = \pi \times {(2.1)^2} \times 2.8 \\
   \Rightarrow v' = 38.808c{m^3} \\
$
Let the number of candles be $n$
Therefore, considering the fact that the Volume of the rectangular solid wax is the same as the total volume of cylindrical candles.
$
   \Rightarrow v = v' \times n \\
   \Rightarrow n = \dfrac{v}{{v'}} \\
   \Rightarrow n = \dfrac{{58212}}{{38.808}} = 1500 \\
$
Therefore, The number of candles is 1500.

Note: The concept of conservation of volume is important in these kinds of problems. It states that a certain quantity will remain the same despite adjustment of the container, shape, or apparent size. In the above case, the volume of the wax container is the same as that of the cylindrical candles even after molding the wax into candles.