An open metal bucket is in the shape of a frustum of a cone of height 21 cm with raddi of its lower and upper ends as 10 cm and 20cm respectively. Find the cost of milk which can completely fill the bucket at Rs. 30 per litre. $\left( use\ \pi =\frac{22}{7}\right)$
Given: a frustum shaped open milk bucket, its height h= 21cm and radii of its lower and upper ends respectively$\ r=10\ cm\ $and$\ R=20\ cm$ and cost of milk $=Rs. 30$ per litre.
To do: To find the total cost of the milk to fill the given bucket completely.
Solution:
We know that volume of a frustum with radii of its lower and upper ends respectively r and R and a height h,$\ =\frac{\pi }{3} \ h( r^{2}+R^{2}+rR)$
Here radii of the lower end,$\ r=10\ cm$
Radii of its upper end, $R=20\ cm$
Height of the bucket, $h=21\ cm$
Volume of the given frustum shaped bucket,$\ V=\frac{\pi }{3} \times 21\left( 10^{2} +20^{2} +10\times 20\right)$
$=\frac{22}{7} \times \frac{1}{3} \times 21( 100+400+200)$
$=15400\ cm^{3}$
$=\frac{15400}{1000} \ litre $
$(As \ known \ that \ 1\ litre=1000\ cm^{3} )$
$=15.4\ litre$
Here given cost of milk$=Rs.\ 30$ per litre
$\therefore$ Total cost of milk to fill the given bucket completely$=15.4\times 30$$=Rs.\ 462$
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