A container in the shape of a frustum of a cone having diameters of its two circular faces as 35 cm and 30 cm and vertical height 14 cm, is completely filled with oil. If each $c m^{3}$ of oil has mass 1.2 g then find the cost of oil in the container if it costs Rs 40 per kg.

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Solution

We have,

Height, h = 14 cm,

Radius of upper end, R = $\frac{35}{2}$ =17.5cm
and

Radius of lower end, r = $\frac{30}{2}$ =15cm

Now, volume of the container = $\frac{1}{3}$ $\times$ $π$ h[ $R^{2}$ + $r^{2}$ + Rr]

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

= $\frac{44}{3}$ × (306.25+225+262.5)

= $\frac{44}{3}$ ×793.75

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

So, the mass of the oil that is completely filled in the container = $\frac{34925}{3}$ ×1.2

= 13970 kg

= 13.97 kg

Therefore, The cost of the oil in the container = 40 x 13.97 = Rs. 558.80

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