Answer :

Given: depth of bucket = height of bucket/frustum = h = 24 cm


Diameter of lower circular end = 10 cm


Diameter of upper circular end = 30 cm


Radius of lower circular end = r = 10/2 = 5 cm


Radius of lower circular end = R = 30/2 = 15 cm


Cost of 100 cm2 metal sheet = 10 Rs


Cost of 1 cm2 metal sheet = 10/100 = 0.1 Rs


Cost of 1 litre milk = 20 Rs



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


Where l = slant height




l = 26 cm


Since 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 × (52 + (15 + 5)26) cm2


= 3.14 × 545 cm2


= 1711.3 cm2


1711.3 cm2 metal sheet is required to make the container.


Cost of 1711.3 cm2 metal sheet = 1711.3 × cost of 1 cm2 metal sheet


= 1711.3 × 0.1 Rs


= 171.13 Rs


Cost of metal sheet required to make container = 171.13 Rs


Now,


Volume of milk which can completely fill the bucket = volume of frustum



= (1/3) × 3.14 × 26 × 325 cm3


= 26533/3 cm3


= 8844.33 cm3


Now 1 litre = 1000 cm3


8844.33 cm3 = 8844.33/1000 litres


= 8.84433 litres


Volume of milk which can completely fill the bucket = 8.84433 litres


Cost of milk which can completely fill the bucket = volume of milk which can completely


fill the bucket × cost of 1 litre milk Rs


= 8.84433 × 20 Rs


= 176.8866 Rs


Cost of milk which can completely fill the bucket = 176.8866 Rs


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