A bucket made up of a metal sheet is in the form of a frustum of a cone . Its depth is 24 cm and the diameters of the top and the bottom are 30 cm and 10cm. Find the cost of milk which can completely fill the bucket at the rate of 20/l and the cost of the metal sheet used if it costs RS 10/100cm2
Answers
Height of frustum of cone = 24 cm
Diameter of top = 30cm
Radius of top = 15cm
Area of top(A1) = (pi)r2
=22/7*(15)2
=707.14 cm2
Diameter of bottom = 10 cm
Radius of bottom = 5 cm
Area of bottom(A2) = (pi)r2
=22/7*(5)2
=78.57 cm2
Volume of frustum of cone =
1/3h(A1+A2+√A1A2)
=1/3*24*
(707.14+78.57+√707.14*78.57)
=8(1021.42)
=8171.37 cm3
Capacity of frustum = 8.1 L (since 1000cm3= 1L)
Cost of milk for 1L = Rs.20
Cost of milk for 8.1L = 20*8.1
= Rs.162
Area of metal sheet used =
Area of bottom of bucket+C.S.A of bucket
=(pi)R22+
(pi)(R1+R2)√(R1-R2)2+h2
=22/7*52+
22/7*(15+5)√(15-5)2+(24)2
=550/7 +
22/7*20√100+576
=550/7 +
440/7√676
=550/7 +
440/7*26
=550+11440/7
=11990/7
=1712.85 cm2
Cost of metal sheet for 100cm2= Rs. 10
Cost of metal sheet for 1712.85 cm2=
10*1712.85/100
=Rs 171.28