# 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,

Question:

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 40 per kg.

Solution:

We have,

Height, $h=14 \mathrm{~cm}$,

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

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

Now,

Volume of the container $=\frac{1}{3} \pi h\left(R^{2}+r^{2}+R r\right)$

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

$=\frac{44}{3} \times(306.25+225+262.5)$

$=\frac{44}{3} \times 793.75$

$=\frac{34925}{3} \mathrm{~cm}^{3}$

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

$=13970 \mathrm{~kg}$

$=13.97 \mathrm{~kg}$

$\therefore$ The cost of the oil in the container $=40 \times 13.97=₹ 558.80$