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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Updated on: 10-Oct-2022

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