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A bucket open at the top, and made up of...

A bucket open at the top, and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of Rs 10 per Crn . | USe TC-3. f metal sh d in itat th f Rs 10 per 100 cm“. [U 3.14

Text Solution

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Radius of the upper end, R = 15 cm.
Radius of the lower, r = 5 cm.
Depth of the bucket, h = 24 cm.
Slant height of the bucket, `l=sqrt(h^(2)+R+r^(2))`
`=sqrt((24)^(2)+(15-5)^(2))`
`=sqrt(676)cm=26 cm`.
Area of metel sheet used
= curved surface area + area of the bottom
`=pi//(R+r)+pir^(2)`
`=[3.14xx26xx(15+5)+3.14xx5xx5]cm^(3)`
`=(3.14xx26xx20xx3.14xx25)cm^(2)`
`=[3.14xx(520+25)cm^(2)=(3.14xx545)cm^(2)=1711.3 cm^(2)`.
`:." cost of metal sheet used"=₹((1711.3)/100xx10)=₹171.13.`
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