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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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 cm3 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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