Based on the balance given below.find the total weight each fruit.the total weight of the fruits is 960g as shown
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Answer:
Answer
Let r be the radius and h be the height of the cylinder of given volume, v.
Now,
v=π
2
h
h=
πr
2
v
…… (1)
As the cylinder is open at the top, so the total surface area is,
s=2πrh+πr
2
s=2π(
πr
2
v
)+πr
2
s=
r
2v
+πr
2
dr
ds
=−
r
2v
+2πr …… (2)
For total surface area to be minimum,
dr
ds
=0
⇒−
r
2
2v
+2πr=0
v=πr
3
πr
2
h=πr
3
⇒h=r
Differentiate equation (2) with respect to r.
dr
2
d
2
s
=
r
3
4v
+2π
⇒(
dr
2
d
2
s
)
r=h
=
h
3
4v
+2π>0
Hence, when the height of the cylinder is equal to the radius of the base of the cylinder, the surface area is minimum.
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