a conical paper cup is in the form of a right circular cone with height 5 cm and diameter of base 4cm.how much water can it hold? plzzz fast response with correct answer will be marked as brainlist
Answers
Answered by
2
Step-by-step explanation:
Explanation:
Let us set up the following variables:
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⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎩
R
Radius of conical cup (cm)
=
30
c
m
H
Height of the conical cup (cm)
=
10
c
m
t
time
(s)
h
Height of water in cup at time t
(cm)
r
Radius of water at time t
(cm)
V
Volume of water at time t
(cm
3
)
Our aim is to find
d
V
d
t
when
h
=
9
and we are given
d
h
d
t
=
2
By similar triangles we have
r
:
h
=
R
:
H
∴
r
h
=
30
10
⇒
r
=
3
h
The volume of a cone is
1
3
π
r
2
h
, So:
V
=
1
3
π
r
2
h
=
1
3
π
(
3
h
)
2
h
=
1
3
π
9
h
2
h
=
3
π
h
3
Differentiating wrt
h
we get:
d
V
d
h
=
9
π
h
2
And Applying the chain rule we have:
d
V
d
t
=
d
V
d
h
⋅
d
h
d
t
=
9
π
h
2
⋅
2
=
18
π
h
2
And so when h=9 we have:
[
d
V
d
t
]
h
=
9
=
18
π
(
9
2
)
=
1458
π
c
m
3
s
−
1
Answered by
3
this Ur answer
this much water it can hold
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