Question

A milk container is made of metal sheet in the shape of frustum of a cone whose volume is 10459 `3/7` cm³. The radii of its lower and upper circular ends are 8cm and 20cm. find the cost of metal sheet used in making container at rate of  Rs 1.4  per cm²?

Answer 1

Given that,

The radii of the top and bottom circles of the container are r₁ =20 cm and r₂ =8 cm.

Let  the depth of the container be h.

Volume of the container

`V = 1/3pi(r_1^2+r_2^2+r
_1r_2)h`

`=1/3xx22/7(20^2+8^2+20xx8)xxh`

`=1/3xx22/7(400+64+160)xxh`

`=1/3xx22/7xx624xxh`

It is given that volume of the cone is 10459`3/7 cm^3`.

`rArr   1/3xx22/7xx624xxh = 73216/7`

`rArr   h = (73216xx3xx7)/(7xx22xx624)`

`= 73216/4576`

`rArr  h = 16 cm`

Hence, the height of container is 16 cm.

The slant height of container

`l=sqrt(h^2+(r_1-r_2)^2)`

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

`=sqrt(256+144)`

`=sqrt(400)`

= 20 cm

The surface area of the used metal sheet to make the container

`S = pi(r_1+r_2)xxl+pir_2^2`

`=22/7xx(20+8)xx20+22/7xx8^2`

`=22/7xx28xx20+22/7xx64`

= 1760 + 201.14

= 1961.14 cm²

The cost of metal sheet used in making the container 

= 1961.14 x 1.40

Rs 2745.59