A bucket made up of a metal sheet is in the form

Solution:

The height of the bucket is h=16cm. The radii of the upper and lower circles of the bucket are r1 =20 cm and r2 = 8 cm respectively.

The slant height of the bucket is

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

$=\sqrt{(20-8)^{2}+16^{2}}$

$=\sqrt{400}$

 

$=20 \mathrm{~cm}$

The volume of the bucket is

$V=\frac{1}{3} \pi\left(r_{1}^{2}+r_{1} r_{2}+r_{2}^{2}\right) \times h$

$=\frac{1}{3} \pi\left(20^{2}+20 \times 8+8^{2}\right) \times 16$

$=\frac{1}{3} \times 3.14 \times 624 \times 16$

$=3.14 \times 208 \times 16$

 

$=10449.92 \mathrm{~cm}^{3}$

Hence the volume of the bucket is $10449.92 \mathrm{~cm}^{3}$

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

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

$=\pi \times(20+8) \times 20+\pi \times 8^{2}$

$=\pi \times 28 \times 20+64 \pi$

 

$=624 \pi \mathrm{cm}^{2}$

Therefore, the total cost of making the bucket is

$=\frac{624 \pi}{100} \times 20$

$=\operatorname{Rs} .391 .9$