Question

A bucket open 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 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of Rs 10 per $100c{m}^2.[Use\pi =3.14]$

Answer 1

Diameter of upper end of bucket = 30 cm
$\therefore$ Radius $\left(r_1\right)$ of upper end of bucket = 15 cm
Diameter of lower end of bucket = 10 cm
$\therefore$ Radius $\left(r_2\right)$ of lower end of bucket = 10 cm
Height(h) of bucket = 24 cm
Slant height (l) of frustum $=\sqrt{(r_1-r_2{)}^2+h^2}$
$=\sqrt{(15-5{)}^2+(24{)}^2}=\sqrt{(10{)}^2+(24{)}^2}=\sqrt{100+576}$
$=\sqrt{676}=26cm$
Area of metal sheet used to make the bucket $=\pi (r_1+r_2)l+\pi r_2^2=\pi (15+5)26+\pi (5{)}^2=520\pi +25\pi =545\pi c{m}^2$
Cost of $100c{m}^2$ metal sheet = Rs 10
Cost of $545\pi c{m}^2$ metal sheet =$Rs\frac{545\times 3.14\times 10}{100}=Rs.171.13$
Therefore, cost of metal sheet used to make the bucket is Rs 171.13