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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 20 per litre and the cost of metal sheet used if it costs 10 per 100 cm². [Use π = 3.14.]
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Answer:
Let r=5 cm R=15 cm and h=24 cm from given data.
I= h^2 +(R−r)^2
=√(24)^2+10)^2cm
= √576+100 cm
= √676 cm
=26 cm
Volume of bucket = volume of frustum
= 1/3 ×πh(R^2+r^2+Rr)
= 1/3ˣ3.14ˣ24ˣ[(15)^2+(5)^2+15ˣ5]
= (25.12×325) cm^3
= 8164 cm^3 =8.164 litres
Cost of milk =Rs. 20×8.164=Rs. 163.28
Total surface area of the bucket:
=π(R+r)+πr ^2
=(3.14×26×(15+5)+3.14×5×5)
= 1711.3 cm^2
Cost of metal sheet = 10× 100/1711.3
= 171.13 Rs.
Hope it helps you!!
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