Answer :

Given: height of container frustum = h = 16 cm


Radius of lower circular end = r = 8 cm


Radius of upper circular end = R = 20 cm


Cost of 100 cm2 metal sheet = 15 Rs


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


Formula: Total surface area of frustum = πr2 + πR2 + π(R + r)l cm2


Where l = slant height




l = 20 cm


Since it is given that a bucket is to be made hence the top is open we need to subtract the area of top/upper circle from total surface area of frustum because we don’t require a metal plate for top.


Radius of top/upper circle = R


Area of upper circle = πR2


area of metal sheet used = (total surface area of frustum)-πR2


= πr2 + πR2 + π(R + r)l- πR2 cm2


= πr2 + π(R + r)l cm2


= π × (82 + (20 + 8)20) cm2


= 3.14 × 624 cm2


= 1959.36 cm2


1959.36 cm2 metal sheet is required to make the container.


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


= 1959.36 × 0.15 Rs


= 293.904 Rs


Cost of metal sheet required to make container = 293.904 Rs


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