1. Oil is being pumped into a huge cylindrical oil drum with diameter 3 m and length 6 m at a rate of 3 L / s. At what rate is the depth of the oil rising when the depth of the oil is 1 m? Note: 1L = 1000 cm3 3 m 1 m = 100 cm 6 m

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A: Given Height of canonical tank=3 m and Radius of canonical tank =2 m and dvdt=2 m3/min.     .....1

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A: Given:

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A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

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A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

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A: Given

Q: 1. A boy is blowing a spherical balloon at a rate of 50 cm /s. At what rate is the radius of the…

A: This question is based on application of derivative.

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A: Given,  The radius of a sphere decreases at the rate of 1 m/sec  We have to find the rate at which…

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Q: 9. At what rate is soda being sucked out of a cylindrical glass that is 6 in. tall and has a radius…

A: Volume of the cylinder ,V=πr2h ; where 'r' is the Radius and 'h' is depth of the cylinder.

Q: 8. The radius of an inflating balloon in the shape of a sphere is changing at a rate of 3cm/sec. At…

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Q: 10. At what rate is the vertex angle of a right circular cone changing when the radius is 3 ft and…

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A: Given that a reservoir is 90 m long whose cross section is an isosceles trapezoid. The dimensions…

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A: Given : Side of Baseball diamond square =90 ft. Drawing the diagram of the whole situation,

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A: For conical glass, Radius r=5 m, Height h=12 m, Rate of filling dVdt=10 cm3/s.

Q: A vertical cylinder having a circular base of radius ‘r’ and a height of 12 m is filled with water…

A: The cylinder is filled with water at the rate of 1 m/min. To Find: If the depth of water in the…

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Q: The height h and radius r of the base of a straight circular cone are varying at constant rates of…

A: Topic:- application of derivatives

Q: 3. Water is flowing into a vertical cylindrical tank at the rate of 24 cubic ft. /min. if the radius…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

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A:

Q: 2. The radius of a sphere decreases at the rate of 5 m/sec. Find the rate at which the volume…

A: Given that the Radius of sphere decreases at the rate of 5m/sec and radius is 5 m

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Q: 11. Determine precisely how large the number a must be chosen so as to ensure that 1 dr < 0.01. + x2…

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Q: 1. We are inflating a spherical balloon. At what rate is the volume of the balloon changing when the…

A: Since you have asked multiple question (1&amp;2) we will solve the first question for you. . If you…

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A: We need to find the rate at which volume decrease when radius is 3m

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A: Volume of cylinder = πr2h  r= radius of cylinder  h= height of cylinder

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A: Given that, the length L= 9 ft, the rate of filling = 17 ft3/min and the rate of leaking = 0.25…

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Q: 1.) Water is pouring into a conical vessel 15 cm deep and having a radius of 3.75 cm across the top.…

A: step by step clear explanation is given .Have a look

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A: We have to find rate of change of  height of pyramid.Information is given below:

Q: 1. The side of a cube increases at the rate of 12 m/sec. Find the rate at which the volume of the…

A: Our guidelines for multiple questions,answer only first question For other answers , Repost this…

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A:

Q: B. The dimensions of a rectangular solid at a given instant (to) are (a = 13 cm), (b = 9 cm) and (c…

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Q: 2. The volume of a cube decreases at a rate of 10m/sec. Find the rate at which the side of the cube…

A: dVdt=10m3/min, side=2mFormula of volumeV= side3

Q: 4. Water is running out of a conical tank 3 m across the top and 4 m deep at the rate of 2 m3 /min.…

A: given  h = 4 m  (Note: measurement of h is always taken from bottom) r = (3 ÷ 2 ) = 1.5 m dVdt = 2…

Q: 2. A man 1.8 meter tall walks away from a lamp post 4 meter high at a speed of 1.5 m/s. How fast is…

A: We'll answer one question since the exact one hasn't specified. Please re-submit the question you…

Q: 14. As sand leaks out of a hole in a container, it forms a conical pile whose altitude is always the…

A: We have to find the rate at which the sand is leaking out when the height is 10 in.  Or we can say…

Q: 1 A 5 m ladder is leaning against a wall of a house. The bottom of the ladder is pulled away from…

A: Let the bottom of the ladder is x meters away from the wall and the top of ladder is at distance y…

Q: 1. The volume of a cube decreases at a rate of 12 m/sec. Find the rate at which the side of the cube…

A: This question is related to application of derivatives.

Q: 1. The radius of a sphere increases at a rate of 2 m/sec. The rate at which the volume increases…

A: This question is based on the application of derivative.