# 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.

#### 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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#### APPEARS IN

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