Question

A cone with its height equal to the diameter of the base is expanding in volume at the rate of 50 cm®/sec. If the base has area 1 m², the radius is increasing at the rate (A) 0.0025 cm/sec (B) 0.25 cm/sec (C) 1 cm/sec (D) 4 cm/sec​

Answer 1

Answer:

Solution

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Correct option is D)

Let the radius of the cone be r

Let base area =A

Volume of cone =V=

3

1

πr

2

h=

3

1

πr

2

d=

3

1

πr

2

(2r)=

3

2

πr

3

dt

dV

=2πr

2

dt

dr

Given,

dt

dV

=40cm

3

/s,A=πr

2

=1m

2

=10000cm

2

⇒40=2(10000)

dt

dr

⇒

dt

dr

=0.0025