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# 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.

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.

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.
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 $n$
$\Rightarrow v = v' \times n \\ \Rightarrow n = \dfrac{v}{{v'}} \\ \Rightarrow n = \dfrac{{58212}}{{38.808}} = 1500 \\$