A bucket, made of metal sheet, is in the form of a cone whose height is $ 35 \mathrm{~cm} $ and radii of circular ends are $ 30 \mathrm{~cm} $ and $ 12 \mathrm{~cm} $. How many litres of milk it contains if it is full to the brim? If the milk is sold at $ ₹ 40 $ per litre, find the amount received by the person.

Given:

A bucket, made of metal sheet, is in the form of a cone whose height is \( 35 \mathrm{~cm} \) and radii of circular ends are \( 30 \mathrm{~cm} \) and \( 12 \mathrm{~cm} \).

The milk is sold at \( ₹ 40 \) per litre.

To do:

We have to find the number of litres of milk it contains if it is full to the brim and the amount received by the person.

Solution:

Radii of the bucket in the form of frustum of cone $= 30\ cm$ and $12\ cm$

$r_1=30\ cm$

$r_2=12\ cm$

Depth of the bucket $h= 35\ cm$

Therefore,

Capacity(volume) of the bucket $=\frac{1}{3} \pi h(r_{1}^{2}+r_{2}^{2}+r_{1} r_{2})$

$=\frac{1}{3} \times \frac{22}{7} \times 35[(30)^{2}+(12)^{2}+(30 \times 12)]$

$=\frac{110}{3}[900+144+360]$

$=\frac{110}{3} \times 1404$

$=51480 \mathrm{~cm}^{3}$

$=51.48$ litres

Cost of milk per litre $=Rs.\ 40$

Total amount received by the person $=Rs.\ 40 \times 51.48$

$=2059.20$

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Updated on: 10-Oct-2022

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