A bucket made of aluminium sheet is of height $ 20 \mathrm{~cm} $ and its upper and lower ends are of radius $ 25 \mathrm{~cm} $ and $ 10 \mathrm{~cm} $ respectively. Find the cost of making the bucket if the aluminium sheet costs $ ₹ 70 $ per $ 100 \mathrm{~cm}^{2} . $ (Use $ \left.\pi=3.14\right) . $
Given:
A bucket made of aluminium sheet is of height \( 20 \mathrm{~cm} \) and its upper and lower ends are of radius \( 25 \mathrm{~cm} \) and \( 10 \mathrm{~cm} \) respectively.
To do:
We have to find the cost of making the bucket if the aluminium sheet costs \( ₹ 70 \) per \( 100 \mathrm{~cm}^{2} . \)
Solution:
Height of the bucket $h = 20\ cm$
Upper radius of the bucket $r_1 = 25\ cm$
Lower radius of the bucket $r_2 = 10\ cm$
Slant height of the bucket $l=\sqrt{(h)^{2}+(r_{1}-r_{2})^{2}}$
$=\sqrt{20^{2}+(25-10)^{2}}$
$=\sqrt{400+225}$
$=\sqrt{625}$
$=25 \mathrm{~cm}$
Therefore,
Surface area of the bucket $=\pi(r_{1}+r_{2}) l+\pi r_{2}^{2}$
$=\pi[(r_{1}+r_{2}) l+r_{2}^{2}]$
$=3.14[(25+10) \times 25+(10)^{2}]$
$=3.14[35 \times 25+100]$
$=3.14[875+100]$
$=3.14 \times 975$
$=3061.5 \mathrm{~cm}^{2}$
Area of the sheet used $=3061.5 \mathrm{~cm}^{2}$
Cost of alumnium sheet per $100 \mathrm{~cm}^{2}=Rs.\ 70$
Total cost of making the bucket $=Rs.\ \frac{3061.5 \times 70}{100}$
$= Rs.\ 2143.05$
The total cost of making the bucket is Rs. 2143.05.
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