Question

A bucket is $40cm$ in diameter at the top and $28cm$ in diameter at the bottom. Find the capacity of the bucket in litres, if it is $21cm$ deep. Also find the cost of tin sheet used in making the bucket, if the cost of tin is $Rs.1.50$ per sq dm.

Answer 1

Given:

$\Rightarrow r_1=20cm,r_2=14cm$ and $h=21cm$

Now, the required capacity (i.e. volume) of the bucket

$=\frac{\pi h}{3}(r_1^2+r_1{r}_2+r_2^2)$
$=\frac{22\times 21}{7\times 3}({20}^2+20\times 14+{14}^2)$
$=22\times 576c{m}^3$
$=19272c{m}^3$
$=\frac{19272}{1000}litres=19.272litres$
Now,
$l=\sqrt{(r_1-r_2{)}^2+h^2}$
$l=\sqrt{(20-14{)}^2+{21}^2}$
$l=\sqrt{6^2+{21}^2}$
$l=\sqrt{36+441}=\sqrt{477}=21.84cm$
$\therefore$ Total surface area of the bucket (which is open at the top)

$=\pi l(r_1+r_2)+\pi r_2^2$
$=\pi \left[\right(r_1+r_2)l+r_2^2]$
$=\frac{22}{7}\left[\right(20+14)21.84+{14}^2]=2949.76c{m}^2$
$\therefore$ Required cost of the tin sheet at the rate of $Rs.1.50$ per $d{m}^2$ i.e. $100c{m}^2$

$=\frac{1.50\times 2949.76}{100}\approx Rs.44.25$