Question

A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the bucket if the cost of metal sheet used is Rs 15 per 100 $c{m}^2$. $[Use\pi =\mathrm{3.14.}]$

Answer 1

Height of the bucket, h = 16 cm (Given)

Let the radii of the upper and lower ends of the bucket be $r_1$ and $r_2$ respectively.

Given, $r_1$ = 20 cm and $r_2$ = 8 cm.

Slant height of bucket , l $=\sqrt{h^2+(r_1-r_2{)}^2}=\sqrt{{16}^2+(20-8{)}^2}=\sqrt{{16}^2+{12}^2}=\sqrt{256+144}==\sqrt{400}=20cm$

Surface are of bucket

= Curved surface area of the bucket + Area of base of the bucket

$=\pi (r_1+r_2)l+\pi r{2}^2=\pi \left[\right(r_1+r_2)l+r{2}^2]=\frac{22}{7}\left[\right(20cm+8cm)20cm+(20cm{)}^2]=\frac{22}{7}(28\times 20c{m}^2+400c{m}^2)=\frac{22}{7}(560c{m}^2+400c{m}^2)=\frac{22}{7}\times 960c{m}^2=3017.14c{m}^2$ (Approx)

Given, cost of 100 $c{m}^2$ metal sheet = Rs 15

Cost of the bucket $=\frac{15}{100}\times 3017.14=452.60$ (Approx)

Thus, the cost of the bucket is approximately Rs 452.60.