A container, open at the top and made up of metal sheet, is in the form of a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 40 cm, respectively. Find the cost of metal sheet used to make the container, if it costs ₹10 per 100 cm^{2}

#### Solution

We have,

Radius of the upper end, `"R" = 40/2 = 20 "cm" and`

Radius of the lower end ,` "r" = 16/2 = 8 "cm"`

Also, the slant height, `l = sqrt(("R" - r)^2 + "h"^2)`

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

`= sqrt(12^2+16^2)`

`=sqrt(144+256)`

`=sqrt(400)`

`= 20 "cm"`

Now,

Total surface area of the container `"l" =sqrt("R"-"r")^2 + "h"^2`

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

`=sqrt(12^2+16^2)`

`=sqrt(144+256)`

`=sqrt(400)`

= 20 cm

Now,

Total surface area of the container = π (R + r) l + πr^{2 }

`= 22/7xx(20+8)xx20+22/7xx8xx8`

`= 22/7 xx 28 xx 20 + 22/7xx64`

`=22/7xx560xx22/7xx64`

`=22/7 xx 624`

`= 13728/7 "cm"^2`

So , the cost of metal sheet used `= 13728/7xx10/100`

`=13728/70`

≈ ₹ 196.11

Hence, the cost of metal sheet used to make the container is ₹196.11.

Disclaimer: The answer given in the textbook is incorrect. The same has been corrected above.