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Question
A bucket made up of a metal sheet is in form of a frustum of cone of height 16cm with diameters of its lower and upper ends as 16cm and 40cm. find the volume of bucket. Also find cost of bucket if the cost of metal sheet used is Rs 20 per 100 cm2
Solution
The radii of the upper and lower circles of the bucket are r1 = `40/2` = 20 cm and r2 = `16/2` =8 cm The height of the bucket (h) = 16 cm.
The slant height of the bucket
`l=sqrt(h^2+(r_1-r_2)^2)`
`=sqrt(16^2+(20-8)^2`
`=sqrt(256+144)`
l = 20 cm
The Volume of the bucket
`V=1/3pi(r_1^2+r_1r_2+r_2^2)xx16`
`=1/3xx3.14(20^2+20xx8+8^2)xx16`
`=1/3xx3.14(400+160+64)xx16`
`=1/3xx3.14xx624xx16`
= 10449.92 cm3
The surface area of the used metal sheet to make the bucket
`S=pi(r_1+r_2)xxl+pi r_2^2`
= π (20+8) x 20 + π x 82
= 560π + 64π
= 624π cm2
Therefore, the total cost of making the bucket
`=(624pi)/100xx20`
`=624/100xx3.14xx20`
Rs 391.87.
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