Q30 of 49 Page 1

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 26 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 100 cm2. [use π = 3.14]

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Given-


Depth of bucket, h = 24 cm


Radius of top bucket(R) = 30/2 = 15 cm


Radius of bottom bucket(r) = 10/2 = 5 cm


∴ Slant height(l) is given by-




⇒ l= √(576+100)


⇒ l= √676


∴ l = 26 cm


Total surface area of bucket (excluding the upper end)


= πl(R+r) + πr2


= 3.14× 26× (15+5) + 3.14× 25


= 1632.8+78.5


= 1711.3 cm2


Cost of 100 cm2 metal sheet = Rs 10


∴ Cost of 1711.3 cm2 metal sheet = (10/100) × 1711.3


= Rs 171.13


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