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# 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

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In given problem a bucket made up of a metal sheet is in the form of a frustum of a cone. To find answer of this question use pathogroups theorem.

Problem from RS Aggarwal book, problem number 8, page number 823, exercise 17C, chapter volume and surface area of solid.
Chapter Mensuration

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1. Solution

given data

Radius of lower circular end = r = 8 cm

Radius of upper circular end = R = 20 cm

Height of container frustum = h = 16 cm

Cost of 100 cm2 metal sheet = rs. 15

Cost of 1 cm2 metal sheet = 15/100 = Rs. 0.15

Slant height,

l2 = (R-r)2 + h2

l2 = (20-8)2 + 162

l2 = 144 + 256

l2 = 400

l = 20 cm

Area of metal sheet used = (Total surface area of frustum)- (Area of upper circle) …(1)

Area of upper circle = πR2

Total surface area of frustum = πr2 + πR2 + π(R + r)l

Area of metal sheet used = (πr2 + πR2 + π(R + r)l) – πR2

= πr2 + π(R + r)l

= π(82 + (20 + 8)20)

Area of metal sheet used = 1959.36 cm3

Cost of 1959.36 cm2 metal sheet = 1959.36 × cost of 1 cm2 metal sheet

= 1959.36 × Rs. 0.15

∴ cost of the bucket if the cost of metal sheet used is Rs. 15 per 100 cm² is Rs.293.904

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