a container opened at the top and made up of a metal sheet is in the form of a frustum of a cone of a height 16cm with radii of its lower and upper ends as 8cm and. 20cm respectively find the cost of a milk which can completely fill the container at the rate of 50 per litre also find the cost of metal sheet used to make the container if it's costs 10 per 100cm²
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Let l be the slant height of the frustum
We have
r
1
=20cm,r
2
=8cm;h=16cm
∴l=
(r
1
−r
2
)
2
+h
2
⇒l=
(20−8)
2
+16
2
=20cm
Now, volume of the container
=
3
1
π(r
1
2
+r
2
2
+r
1
r
2
)h
=
3
1
π(20
2
+8
2
+20×8)×16cm
3
=
3
3.14×624×16
cm
3
=10449.92cm
3
=10.45litres
Cost of milk at the rate of 15 Rs. per litre =Rs.(10.45×15)=Rs.156.75
Total surface area of the frustum =π(r
1
+r
2
)l+πr
2
2
={3.14(20+8)×20+3.14×8
2
}cm
2
=3.15×(560+64)cm
2
=3.14×624cm
2
=1959.36cm
2
Cost of metal used =Rs.(
100
1959.36×5
)=Rs.97.96
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