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=(R−r)2+h2 =(20−8)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