Question

A Bucket of height $16cm$ is made up of metal sheet in the form of frustum of right circular cone with radii of its lower end upper ends as $8cm$ and $20cm$ respectively. Find the volume of milk which can be filled in the bucket. Also find the cost of making the bucket when the metal sheet costs $RS15$ per $100c{m}^2$.

Answer 1

Given that:

$h=16cm,R=20cm,r=8cm$

If $l$ be the slant height of frustum

Then $l=\sqrt{h^2+(R-r{)}^2},$

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

$l=\sqrt{256+144}=20cm.$

Now,

Curved surface area of the frustum $=\pi l(R+r)$

$=\pi \times 20(20+8)=1760c{m}^2$

Total metal sheet required $=C.S.A+Areaofbase$

$=1760+\frac{22}{7}\times 8^2$

$=1760+201.14$

$=1961.14c{m}^2$

Cost of total metal sheet $=1961.14\times \frac{15}{100}=Rs.294.17$