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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` 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?
Solution
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
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