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Question
A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16 cm and radii of its lower and upper ends are 8 cm and 20 cm, respectively. Find the cost of the bucket if the cost of metal sheet used is Rs 15 per 100 cm2.
Solution
Greater radius of the frustum = R = 20 cm
Smaller radius of the frustum = r = 8 cm
Height of the frustum = h = 16 cm
Slant height, l, of the frustum
`=sqrt("h"^2+("R"^2-r^2))`
`=sqrt(16^2 + (20-8)^2)`
`=sqrt(256+(12)^2)`
`=sqrt(256+144)`
`=sqrt(400) = 20 "cm"`
Surface area of the frustum
= πr2 + πl(R + r)
= π[r2+l(R+r)]
`=22/7 [64+20(28)]`
`=(22xx624)/7 = 1961.14 "cm"^2`
100 cm2 of metal sheet costs Rs 15.
So, total cost of the metal sheet used for fabrication
`= 1961.14/100 xx 15`
`="Rs" 294.171 `
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