Question

A bucket made up of a metal sheet is in the form of a frustum of a cone of height $16$ cm and radii of its lower and upper ends are $8$ cm and $20$ cm respectively. Find the cost of the bucket if the cost of metal sheet used is Rs. $15$ per $100c{m}^2$

Answer 1

Radius of lower circular end $=r=8cm$
Radius of upper circular end $=R=20cm$
height of container frustum $=h=16cm$
Cost of $100c{m}^2$ metal sheet $=Rs.15$
cost of metal sheet used $=15/100=Rs.0.15$
slant height, $l^2=(R-r{)}^2+h^2$
$=(20-8{)}^2+{16}^2$
$=144+256$
$=400$
or $l=20cm$

Now of metal sheet used =(Total surface area of frustum)(Area of upper circle)$..\left(i\right)$
Area of upper circle = $\pi R^2$
Total surface area of frustum = $\pi r^2+\pi R^2+\pi (R+r)lc{m}^2$
$\left(1\right)$
Area of metal sheet used = $(\pi r^2+\pi R^2+\pi (R+r\left)l\right)-\pi R^2$
$=\pi r^2+\pi (R+r)l$
$=\pi (8^2+(20+8\left)20\right)$
$=1959.36c{m}^3$
Again,
cost of $1959.36c{m}^2$ metal sheet $=1959.36$ x cost of $1c{m}^2$ metal sheet
$=1959.36\times Rs.0.15$
$=Rs.293.904$