This is one of the very important question from the cbse board exam point of view because in 2008, 2006, 2009 cbse board exam this question was asked. Question number 9 from RS Aggarwal book page number 823, exercise 17C, chapter volume and surface area of solid.
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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 completely filling the bucket with milk at the rate of Rs 20 per liter and the cost of metal sheet used if it costs Rs 10 per 100 cm²
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Solution
given data,
Greater diameter of the bucket = 30 cm
Radius of the bigger end of the bucket = R = 15 cm
Diameter of the smaller end of the bucket = 10 cm
Radius of the smaller end of the bucket = r = 5 cm
Height of the bucket = 24 cm
Slant height,
l = √ (h²+[R-r]²)
= √ (24²+[15-5]²)
= √ (576+102)
= √ (576+100)
= √676
l = 26 cm
Capacity of the frustum = [1/3] π h [R²+r²+rR]
= [1/3]×3.14×24 [15²+5²+15×5]
=3.14×8×325
=8164 cm³
=8.164 liters ( 1000 cm³ = 1 liter )
A litre of milk cost Rs 20.
total cost of filling the bucket with milk
=8.164×20
∴ total cost of filling the bucket with milk = Rs 163.28
Surface area of the bucket =πr²+πl [R+r]
= π (r²+ l [R+r] )
=π (5² + 26[15+5]
=3.1425+2620
=3.1425+520
=1711.3 cm²
Cost of 100 cm² of metal sheet is Rs 10.
∴ cost of metal used for making the bucket =1711.3100×10=
∴ cost of metal used for making the bucket is Rs 171.13