A bucket made of a aluminium sheet is of height 20 cm
Question:

A bucket made of a aluminium sheet is of height 20 cm and its upper and lower ends are of radius 25 cm and 10 cm respectively. Find the cost of making the bucket if the aluminium sheet costs Rs 70 per 100 cm2 . (Use π = 3.14).

Solution:

The height of the bucket is 20cm. The radii of the upper and lower circles of the bucket are r1 =25cm and r2 =10cm respectively.

The slant height of the bucket is

$l=\sqrt{\left(r_{1}-r_{2}\right)^{2}+h^{2}}$

$=\sqrt{(25-10)^{2}+20^{2}}$

$=\sqrt{625}$

$=25 \mathrm{~cm}$

The surface area of the used aluminium sheet to make the bucket is

$S_{1}=\pi\left(r_{1}+r_{2}\right) \times l+\pi r_{2}^{2}$

$=\pi \times(25+10) \times 25+\pi \times 10^{2}$

$=\pi \times 35 \times 25+100 \pi$

$=3061.5 \mathrm{~cm}^{2}$

Therefore, the total cost of making the bucket is

$=\frac{3061.5}{100} \times 70$

$=2143.05$

Hence the total cost is Rs.2143.05