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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. - Mathematics


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.

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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


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


`= sqrt(144+256`


`= 20  "cm"`


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

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




`=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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RS Aggarwal Secondary School Class 10 Maths
Chapter 19 Volume and Surface Area of Solids
Exercise | Q 38 | Page 916
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