A bucket made up of a metal sheet is in the form of frustum of a cone. Its depth is 24 cm and the diameters of the top and bottom are 30 cm and 10 cm respectively. Find the cost of milk which can completely fill the bucket at the rate of Rs 20 per litre and the cost of metal sheet used if it costs Rs 10 per 100 cm2. [Use π = 3.14.]

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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