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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?
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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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