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Question

A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of Rs.44 per litre which the container can hold.


Solution

We are given,
h=16 cm,r1=20 cm,r2=8 cm
Volume of frustum of the cone

=13πh(r21+r22+r1r2)

=13×3.14×16×(202+82+20×8)=10450 cm2

Since,


1000 cm3=1L;10450 cm3=11000×10450=10.45L 
Cost of 1l of milk= Rs20
Cost of 10.45l of milk= Rs(20×10.45) = Rs 209


Total surface area of the frustum of the cone

=π(r1+r2)h2+(r1r2)2+πr21+πr22

=3.14(20+8)162+(208)2+π202+π82=3215 cm2

Cost of100cm2of metal sheet =Rs8
Cost of3215cm2of metal sheet

=π(r1+r2)h2+(r1r2)2+πr21+πr22

rs8100×3215=Rs.250

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