Question

If water is poured into an inverted hollow cone whose semi-vertical angle is 30°, its depth increases at the rate of 2 cm/s. Rate at which the volume of water increases when the depth is 6 cm is λπ cm3/sec. The value of λ is

Answer 1

Step-by-step explanation:

Let the height of cone =h

Radius =r

θ

°

=30°

According to question,

dt

dh

=1cm/sec

tanθ=

h

r

⇒

3

1

=

h

r

⇒r=

3

h

−−−−−(1)

Now,

dt

dv

=

dt

d

(

3

1

πr

2

h)=

3

1

π

dt

d

(r

2

h)

Using (1)

dt

dv

=

3

1

π

dt

d

(

3

h

2

h)=

3

1

π⋅

3

1

dt

d

(h

3

)

dt

dv

=

9

1

π⋅3h

2

dt

dh

=

3

π

h

2

dt

dh

When h=24cm

dt

dv

=

3

π

⋅24⋅24⋅(1)=

192πcm

2

/sec

Answer 2

Step-by-step explanation:

ans in pic hope it's a helpful