Question

A bucket opens at the top, and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is $24cm$ and the diameters of its upper and lower circular ends are $30cm$ and $10cm$ respectively. Find the cost of metal sheet used in it at the rate of $Rs10$ per $100c{m}^2$. $[Use\pi =3.14]$.Insert answer in nearest integer.

Answer 1

Diameter of upper end of bucket = $30cm$

Diameter of lower end of bucket = $10cm$

Then, radius of upper end of bucket $r_1=\frac{30}{2}=15$ cm

And, radius of lower end of bucket $r_2=\frac{10}{2}=5$ cm

Height of bucket = $24cm$

Slant height of bucket = $\sqrt{(r_2-r_1{)}^2+h^2}$

$=\sqrt{(15-5{)}^2+(24{)}^2}=\sqrt{(10{)}^2+(24{)}^2}$

$=\sqrt{100+256}=\sqrt{676}=26cm$

Area of metal sheet used to make bucket

$=\pi (r_1+r_2)l+\pi (r_2{)}^2=\pi (15+5)26+\pi (5{)}^2$

$=520\pi +25\pi =545\pi c{m}^2$

Given cost of $100$ sq cm metal sheet =Rs.$10$

Cost of $545\pi c{m}^2$ metal sheet $=\frac{545\times 3.14\times 10}{100}=171.13Rs.$

Cost of metal sheet used for making bucket $=Rs.171.13$