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 are 8 cm and 20 cm, respectively. Find the cost of the bucket if the cost of metal sheet used is Rs 15 per 100 cm². [Use π = 3.14.]

Answer 1

Greater radius of the frustum = R = 20 cm

Smaller radius of the frustum = r = 8 cm

Height of the frustum = h = 16 cm

Slant height, l, of the frustum

`=sqrt("h"^2+("R"^2-r^2))`

`=sqrt(16^2 + (20-8)^2)`

`=sqrt(256+(12)^2)`

`=sqrt(256+144)`

`=sqrt(400) = 20  "cm"`

Surface area of the frustum

= πr² + πl(R + r)

= π[r² + l(R + r)]

`=22/7 [64+20(28)]`

`=(22xx624)/7 = 1961.14  "cm"^2`

100 cm² of metal sheet costs Rs 15.
So, total cost of the metal sheet used for fabrication

`= 1961.14/100 xx 15`

`="Rs"  294.171 `