47. The volume of a cantaloupe is approximated by v = far'. The radius is growing at the rate of 0.7 cm/week, at a time when the radius is 7.5 cm. How fast is the volume changing at that moment?

Q: Suppose the edges of a cube are increasing at a constant rate of 8 m/hr. Then, the volume of the…

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Q: A fluid is being pumped from a cylinder into a rectangular prism with a square base. The base has…

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Q: 3. The radius of a spherical balloon is increasing at the rate of 2 cm per minute. How fast is the…

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Q: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.1 cm/min.…

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Q: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.1 cm/min.…

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Q: 7) A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15…

A: Given: A spherical balloon is to deflated so that its radius decreases at a constant rate of 15…

Q: 3. A cylindrical tank of diameter 20ft is being drained with water at the rate of 400ft /min. How…

A:

Q: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.4 cm/min.…

A: Volume of a sphere of radius r isV=43πr3

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: A balloon leaves the ground 18m from an observer and rises vertically at 1.25 m/s. How fast is the…

A: "Since you have asked multiple questions,we will solve first question for you. If you want any any…

Q: There is a constant outflow of a liquid into a inverted conical vessel 15 m deep and 7.5 m in…

A: Find the rate of change of volume of water in the cone, with respect to time:…

Q: 8. The volume of a right circular cylinder is 60 cm³ and is increasing at 2 cm³/min at a time when…

A: Given:                                 Volume of a right circular cylinder V…

Q: 12. The height of a right circular cone is increasing at 3mm/s and its radius is decreasing at…

A: Volume of a right circular cylinder is given by formula,  V=πr2h , where r is the radius of circular…

Q: 16.Suppose that the dimensions of a cylinder change at constant rates: the radius of the base is…

A: Use the derivative and substitute the given values.

Q: The length of the rectangle is increasing at a rate of 5 cm per second, and its width is decreasing…

A: Area of rectangle = Length * Width

Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Differentiate volume wrt t

Q: A spherical snowball is melting in such a way that its volume is decreasing at a rate of 2 cm / min.…

A: Given-  dVdt=-2cm3/min (negative sign indicates that it is decreasing). To find- The rate of radius…

Q: 3. A mixture is transferred into a cylindrical container through a conical filter. If the filter is…

A: The volume of a cone: V=13πr2h Where, r  is the radius of the cone. h is the vertical height of the…

Q: 5) Suppose a liquid is to be cleared of sediment by pouring it through a cone-shaped filter. Assume…

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Q: The length of the rectangle is increasing at a rate of 5 cm per second, and its width is decreasing…

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Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min.…

A:

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: 21. The radius of a spherical balloon is increasing at the rate of 3 centimeters per minute. How…

A:

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

A:

Q: 5. A spherical balloon is inflated so that its volume is increasing at the rate of 2 m'/min. At what…

A: Let r be the radius of the balloon and D be the diameter.

Q: 5. The volume of a cube is increasing at a rate of 10 cm³/min . How fast is the surface area…

A: Given:- The volume of a cube is increasing at a rate of 10 cm³/min. To find:- How fast is the…

Q: A liquid solution is passing thru a conical filter 2 feet deep and 4/3 feet across the top, into a…

A: We have to find the rate at which the level of the solution in the cylinder rising.

Q: 3. The radius of a cylinder is increasing at a rate of 4cm/sec. The surface area remains constant at…

A: Given

Q: 9. A paper cup has shape of a cone with height 10 cm and radius 3 cm (at the top). If water is…

A:

Q: 2. Suppose that the bottom of a conical shaped tank of water has been ruptured. At the instant when…

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Q: 1. Suppose that oil spills from a container and spreads in a circular pattern. If the radius of the…

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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: 17. If the radius of a sphere is increasing at the constant rate of 3 inches per second, how fast is…

A: Given: The radius of the sphere is increasing at the constant rate of 3 inches per second. To find:…

Q: The side of the base of a square prism is decreasing at a rate of 7 km/min and the height of the…

A: Surface area of a square prism is given by- A=2a2+4ah where a is side of prism, h is height of…

Q: 10) Air is being pumped into a spherical balloon so that its volume increases at a rate of 100 cm…

A:

Q: How do you solve question 1?

A: The relation between volume of a sphere and the its radius is given as, Where  V: Volume r: Radius

Q: 4) A particle is moving along the curve y = vx. As the particle passes through the point (4,2), its…

A:

Q: 4. A solid cylindrical cord of elastic material has length 32 inches and radius 0.5 inch. The cord…

A: Given:        Length  l=32 inches        radius  r=0.5 inch      Volume of a cylinder  V=πr2l…

Q: A tank initially contains 100 L of a well-mixed water-and-salt solution, with salt concentration of…

A: As the solution well mixed water and solution solution and flowing out with the constant rate of 2 L…

Q: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.4 cm/min.…

A:

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

A:

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 spherical snowball is melting in such a way that its radius is decreasing at rate of 0.2 cm/min.…

A:

Q: 44. The dimensions of a rectangular plate are changing so that the plate maintain its rectangular…

A: Let the length of Rectangle =x Let the width of Rectangle =y since,  Area = (length)×(width)…

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: 12. If the volume of a spherical balloon is expanding at a rate of 5im; How fast is the 4 radius of…

A:

Q: 5) If the radius of a right circular cylinder is increasing at a rate of 1 inch per minute, and the…

A: The volume of cylinder is given by the formula V=πr2h. The given values are as follows: r=40 inches,…

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 cm/min.…

A: To find the rate of decreasing of the volume when the radius is 10 cm.

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