Question

Water is flowing into a right circular conical vessel, 45 cm deep and 27 cm in diameter at the rate of 11 cm³/min. How fast is the water-level rising when the water is 30 cm deep?



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Answer 1

Answer:

0.043 cm/min

Step-by-step explanation:

Radius = 27 cm

Diameter = 27/2

Height = 45 cm

Rate = 11 cm³/min

Volume of sphere = 1/3πr²h

We know that in a cone ratio of height and radius is fixed at any point of time.

R/H = r/h

R/H = (27/2)/45

r = h × (27/2)/45

r = 3h/10

Volume = 1/3πr²h

Volume = 1/3π × 3h/10 × 3h/10 ×h

Volume = π/3 × (3/10)² × 3h²

Rate = Volume

11 = π × (3/10)² × 30

11/π = 100/3² × 1/30²

11 × (7/22) × 1/81

7/162

Speed = 0.043 cm/min

Hence, the water level is rising 0.043 cm/min.

Answer 2

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