9. A paper cup has shape of a cone with height 10 cm and radius 3 cm (at the top). If water is poured into the cup at a rate of 2 cm /sec, how fast is the water level rising when the water is 5 cm deep?

Q: A water tank in the shape of an inverted cone is being filled up with water at a uniform rate of…

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Q: Water is poured into a conical paper cup at the rate of 3/2 in3/sec (similar to Example 4 in Section…

A: The situation is as shown below: Consider a small differential element of water at a height of h…

Q: Water is poured into a conical paper cup at the rate of 3/2 in/sec (similar to Example 4 in Section…

A: I will use the formula V=13πr2h and differentiation method to solve this problem.

Q: 1. A paper cup has the shape of a cone with height 12 cm and radius 4 cm (at the top). If water is…

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

Q: 1. Water is flowing at the rate of 2 m3/min into a tank in the form of an inverted cone having an…

A: It is given that the cone has altitude 16 m and radius 4 m. That is, hcone=16,rcone=4. Let r and h…

Q: A conical vessel 12 cm deep and with a radius of 6 cm at the top, is being filled with water. If the…

A: A conical vessel 12 cm deep and with a radius of 6 cm at the top. That is, the height of the cone is…

Q: 2. A water tank is in the form of an inverted right circular cone h feet deep and d feet wide across…

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Q: 3. Water is flowing out of a cylindrical storage tank at a rate of 2 m3/min. If the tank has a…

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Q: 2. A water heater that has the shape of a right cylindrical tank with a radius of 2 ft and a height…

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Q: 3 The volume of a cube is increasing at the rate of 8 cm³/sec.How fast is the surface are increasing…

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Q: Water is poured into a conical tank 6 m across the top and 8 m deep at the rate of 10 m3min. How…

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Q: Water is being poured at the rate of 2z m' /min into an inverted conical tank that is 12-meter deep…

A: We need to find rate of water leaking.

Q: A water tank has the shape of a horizontal cylindar with radius 1 and length 2. If water is being…

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Q: 9. When a particular plate of metal is heated in an oven, its radius increases at the rate of…

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Q: Consider a right cylinderical water tank of radius 36 metres. The tank contains water. Water is…

A: Let V be the volume h be the height and r be the radius AlsodVdt=1 m3/sec

Q: A conical water tank has a radius of 3 m and a height of 6 m. Water is flowing into the tank at the…

A: NOTE: Refresh your page if you can't see any equations. . here we have R=3 H=6 V'=12

Q: Water is flowing into a vertical cylindrical tank at the rate of 5 cu ft/min. If the radius of the…

A: Given, water is flowing into a vertical cylindrical tank at the rate of 5 cu ft/min (ie) Volume is…

Q: 4. A cylindrical tank with radius 5 m is being filled with water at a rate of 3 m3/min. How fast is…

A: We know  (V) volume of cylinder =πr2h. r= radius of cylinder h= height of cylinder  V= volume of…

Q: 10. A right circular cone with radius 3 cm and height 6 cm is submerged point first into a tall…

A: We have to find the water level rising at rate of

Q: 4. A water trough is 8 m long, and a cross section has the shape of an isosceles triangle that is…

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Q: A softball diamond is a square whose sides are 60 ft long. Suppose that a player running from first…

A: Suppose , y is the distance from the home and x is the distance from first base. Given that ,…

Q: The sides of a square increase in length at a rate of 4 m/sec. a. At what rate is the area of the…

A: Area of square = a2 Where a is length of side of square.

Q: Water is being poured at the rate of 27 m²/min. into an inverted conical tank that is 12-meter deep…

A:

Q: 1. Water is flowing into a vertical cylindrical tank at the rate of 24 cu. ft. per min. If the…

A: Given , Water is flowing into vertical tank at rate if 24 cu .ft . per min. Radius of tank is 4ft.…

Q: The original 24 m edge length x of a cube decreases at the rate of 2 m/min. a. When x = 1 m, at what…

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Q: A hemispherical tank full of water is emptied by a pipe at the rate 3 4/7 liters per second. How,…

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Q: 3. Water is flowing out of a cylindrical storage tank at a rate of 2m/min. If the tank has a radius…

A:

Q: 4 THE LENGTH OF A TRIANGLE LL INCREASING ATA RATE OF 8cm/s AND ITS WIDTH IS INCREASING AT A RATE OF…

A: SOLUTION-

Q: 5. A baseball diamond has the shape of a square with sides 90 ft long. A player 60 ft from second…

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Q: 2. A cylindrical plastic container with a radius of 15 cm is being filled with orange juice at a…

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Q: How fast is the volume of a cube changing when the edge is 15 cm if the edge is changing at the rate…

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Q: A water trough is 11 feet long, and its cross section is an equilateral triangle with sides 3 feet…

A: (a) Height of side of equilateral triangle with side s is,

Q: A paper cup has the shape of a cone with height 10 cm and radius 3 cm (at the top). If water is…

A: From the given problem the representative diagram is shown as below: Let the radius of the cone be…

Q: Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the…

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Q: 4. A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15…

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Q: Water is pouring into a conical vessel 15 cm deep and having a radius of 3.5 cm across the top. If…

A: Given the water is pouring into a conical vessel of 15 cm deep and the radius of 3.5 cm across the…

Q: 3. The area of a circular inkblot starts from zero and grows at a constant rate of 4n cm/minute.…

A: Use the derivative and formula for area of circle.

Q: A cylindrical tank with radius 5m is being filled with water at a rate of 4 m^3/min. How fast is the…

A: Given:         radius of cylinder (r)=5m         rate of water filled dvdt=4m3/minwe know that…

Q: A bacterial cell is spherical in shape. If the radius of the cell is increasing at the rate of 0.01…

A: Volume of sphere: V = 43πr3, where r is radius of sphere. Surface area of sphere: S = 4πr2, where r…

Q: Suppose that a spherical balloon is being inflated and the radius of the balloon is increasing at a…

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Q: 3. A water tank has the shape of an inverted circular cone with base radius 4 m and height 8 m. If…

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Q: 2. A cylindrical tank standing upright (with one circular base on the ground) has radius 1 meter.…

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Q: Water is poured into a conical paper cup at the rate of 3/2 in/sec (similar to Example 4 in Section…

A: Let the volume of conical paper cup be V in³, radius be r in, height be h in  Given dV/dt=(3/2)…

Q: coffee is draining out of a conical filter at a rate of 2.25 inches cubed per minute. If the cone is…

A: given: coffee is draining out of a conical filter at a rate of 2.25 inches cubed per minute. If the…

Q: A bacterial cell is spherical in shape. If the radius of the cell is increasing at the rate of 0.01…

A: Given , Bacterial cell is in spherical shape.Let radius be 'r' μm . ∴ Volume of cell, v v = 43π…

Q: 2. Air is leaking from a spherical-shaped advertising balloon at the rate of 26 cubic feet per…

A: Let r be the radius and v be the volume of balloon, Given dvdt=26 cf/minuteswe know…

Q: Water flows at the rate of 2000 cubic cm per second into a vertical cylindrical tank 120 cm in…

A: Let height of cylindrical tank is "h". Diameter is 120 cm. So, Radius would be r=1202=60 cm Volume…

Q: 4. A trough filled with liquid is 2 m long and has a cross section of an isosceles trapezoid 30 cm…

A: Given: 4) Question is wrong (Some values are missed) 5) dxdt=10 ft/sec, h=100 ft, and l=125 ft

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.