Rate at which the water level rises or falls in a cylinder, cone or bowl
This type of question, asked 5 times: 10 May 2023 S1, 16 May 2023 S2, 9 May 2024 S2, 13 May 2024 S2, 13 May 2026 S2. All 5 questions below, oldest first.
Try each one first, then open its answer.
Question 1
10 May 2023 S1
110Water is running in a hemispherical bowl of radius 180 cm at the rate of 108 cubic decimeters per minute. How fast the water level is rising when depth of the water level in the bowl is 120 cm? (1 decimeter = 10 cm)Tap an option to check your answer.
Question 2
16 May 2023 S2
111Water is being poured at the rate of 36 into a cylindrical vessel, whose circular base is of radius 3 meters. Then the water level in the cylinder is rising at the rate ofTap an option to check your answer.
Question 3
9 May 2024 S2
135A water tank has a shape of inverted right circular cone whose semi-vertical angle is . Water is poured into it at constant rate of 5 cubic meter/minute. The rate in meter/minute at which level of water is rising, at the instant when depth of water in the tank is 10 m isTap an option to check your answer.
Question 4
13 May 2024 S2
133Water is running in a hemispherical bowl of radius 180 cm at the rate of 108 cubic decimeters per minute. How fast the water level is rising when depth of the water level in the bowl is 120 cm? (1 decimeter cm)Tap an option to check your answer.
Question 5
13 May 2026 S2
76A water tank in the house of an inverted cone is being emptied at the rate of cubic feet per second. The height of the cone is feet and the radius is feet, then the rate of change of the water level when the depth is feet.Tap an option to check your answer.