Hanumappa and his wife Gangavva are busy making Jaggery out of sugar-cane. They have processed the sugar cane juice to make the molasses which is poured into moulds of the shape shown in the figure. It will be cooled to solidify in this shape to be sent to the market. Each mould is in the shape of a frustum of a cone having the diameters of its two circular ends as $30 c m$ and $35 c m$ and the height of the mould is $14 c m$ . If each ${c m}^{3}$ of molasses weighs about $1.2 g m$ , find the weight of molasses that can be poured into each mould (Take $π = 22 / 7$ )

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Solution

Clearly the mould is in the shape of a frustum of a cone with radii of two circular ends as

$r_{1} = \frac{30}{2} c m = 15 c m, r_{2} = \frac{35}{2} c m = 17.5 c m$

Quantity of molasses that can bepoured into it
= volume of the mould

$= \frac{π}{3} h (r_{1}^{2} + r_{2}^{2} + r_{1} r_{2})$

$= \frac{1}{3} \times \frac{22}{7} \times 14 (15^{2} + {17.5}^{2} + 15 \times 17.5) {c m}^{3}$

$= \frac{44}{3} (225 + 306.25 + 262.5) {c m}^{3}$

$= \frac{34925}{3} {c m}^{3}$

It is given that $1 {c m}^{3}$ of molasses has mass $1.2 g m$

The mass of the molasses that can be poured into each mould

$= \frac{34925}{3} \times 1.2 g m$

$= \frac{34925 \times 0.4}{1000} k g$

$= 13.97 k g$

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