Advertisement Remove all ads

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

Sum

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.

Advertisement Remove all ads

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.

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 19 Volume and Surface Area of Solids
Exercise | Q 38 | Page 916
Advertisement Remove all ads

Video TutorialsVIEW ALL [2]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×