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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.
Solution
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.
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