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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 100cm2

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Solution

Radius of lower circular end =r=8cm
Radius of upper circular end =R=20cm
height of container frustum =h=16cm
Cost of 100cm2 metal sheet =Rs.15
cost of metal sheet used =15/100=Rs.0.15
slant height, l2=(Rr)2+h2
=(208)2+162
=144+256
=400
or l=20cm

Now of metal sheet used =(Total surface area of frustum)(Area of upper circle)..(i)
Area of upper circle = πR2
Total surface area of frustum = πr2+πR2+π(R+r)lcm2
(1)
Area of metal sheet used = (πr2+πR2+π(R+r)l)πR2
=πr2+π(R+r)l
=π(82+(20+8)20)
=1959.36cm3
Again,
cost of 1959.36cm2 metal sheet =1959.36 x cost of 1cm2 metal sheet
=1959.36×Rs.0.15
=Rs.293.904

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