Question

A milk container is made of metal sheet in the shape of frustum of a cone whose volume is `"10459"  3/7  "cm"`. The radii of its lower and upper circular ends are 8 cm and 20 cm, respectively. Find the cost of metal sheet used in making the container at the rate of ₹1.40 per cm².

Answer 1

We have, 

Radius of the upper end, R = 20 cm and 

Radius of the lower end, r = 8 cm

Let the height of the container = 10459 `3/7  "cm"^3`

`=> 1/3pi"h"("R"^2 + "r"^2 + "Rr")=73216/7`

`=> 1/3xx22/7xxhxx(20^2+8^2+20xx8) = 73216/7`

`=(22"h")/21 xx(400+64+160)=73216/7`

`=> (22"h")/21 xx 624 = 73216/7`

`=>"h" = (73216xx21)/(7xx22xx624)`

⇒ h = 16 cm

Also,

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

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

`= sqrt(144+256`

`=sqrt(400)`

`= 20  "cm"`

Now,

Total surface area of the container = πl(R+r) +πr²

`= 22/7xx20xx(20+8)+22/7xx8xx8`

`=22/7xx20xx28+22/7xx64`

`=22/7xx(560+64)`

`=22/7xx624`

`=13728/7 "cm"^2`

So, the cost metal sheet `= 1.4 × 13728/7 = ₹ 2745.60`

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