The radius r of a circle is increasing at a rate of 3 centimeters per minute. Find the rate of change of the area when r = 38 centimeter cm²/min

Q: The radius of a circle is increasing at a rate of 4 centimeters per minute. Find the rate of change…

A: Area of circle having radius r is given by:     A=πr2Given rate of change of radius=drdt=4cm/minRate…

Q: The area of a circle is increasing at a rate of 10 ft2/min. Find the rate of change of the diameter…

A: Area of a circle is increasing at a rate of 10ft2/min. To find: Rate of change of diameter, given…

Q: The radius r of a sphere is increasing at a rate of 6 inches per minute. (a) Find the rate of change…

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Q: A cylindrical box has a fixed height of 12 inches. Find the rate of change of volume with respect to…

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Q: The radius r of a right circular cylinder with a fixed height of 48 inches is increasing. Find the…

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Q: The rate of change of the area enclosed between the circle and the square is squa meters per hour.

A: First find difference in area between square and circle then differentiate wrt t

Q: 6. Find the rate of change of the circumference of a circle with respect to the area when (a) the…

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Q: An engineering student is experimenting on a cylindrical can with a fixed rate of 8 inches. Find the…

A: Please check step 2 for the solution.!

Q: The radius r of a circle is increasing at a rate of 3 centimeters per minute. Find the rate of…

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Q: The radius r of a sphere is increasing at a rate of 6 inches per minute. (a)  Find the rate of…

A: Given:The radius r of a sphere is increasing at a rate of 6 inches per minute.

Q: Find the average rate of change of the area of a circle with respect to its radius r as r changes…

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Q: The volume of a sphere is increasing at a rate of 8 cubic cm/sec.  Find the rate of change of its…

A: Let V be the volume of the sphere which is given in the question as,

Q: The radius r of a circle is increasing at a rate of 3 centimeters per minute. Find the rate of…

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Q: The radius r of a circle is changing at the rate of -2/π m/sec. At what rate is the circle’s area…

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Q: The radius R of a circle is increasing at the rate of 1 cm per sec. How fast is the area changing…

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Q: Given a cylinder surmounted on both ends by a hemisphere, find the rate of change of its volume with…

A: Given:     Cylinder is surmounted by hemisphere at both ends.And height of cylinder is 5 meter.

Q: If the radius of a circle increases at the rate of 0.01 inch/sec, find the rate of change of the…

A: We have to find the rate of change of area when the radius is 3 inches and when the radius increases…

Q: The radius of a sphere is increasing at the rate of 2 meters per se of change of the volume with…

A: Given: The radius of a sphere is increasing at the rate of 2 meters per second.

Q: The altitude () of a right triangle is always twice the base (). Find the rate of change of the area…

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Q: Evaluate the rate of change of the Area if the area of the circle is given by A= 6 r² when dr 7 and…

A: Given, the area of circle A=6r2

Q: The area of a square with sides of length s is given by A = s'. Find the rate of change of the area…

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Q: The radius of a circle increases at a rate of 4 cm/ sec. The rate at which the area of the circle…

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Q: The radius of a circle is changing atthe rate of -2/paiA m/sec. At what rate is the circle’s area…

A: Let the radius of the circle be r. Then the area (A) of the circle is: A=πr2 Differentiating with…

Q: The radius of a circle is increasing at a rate of 5 centimeters per minute. Find the rate of change…

A: We can find the answer as below using the given data.

Q: The radius of a sphere decreases at a rate of 8 m/sec. Find the rate at which the surface area…

A: It is given that the radius of sphere decreases at a rate of 8 m/sec. So, drdt=-8. The radius is r=3…

Q: 1. Find the rate of change of the area of a circle with respect to its radius when the radius is 3…

A: Authoring guidelines:…

Q: The volume of a cube with sides of lengths is given by=s. Find the rate of change of volume with…

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Q: The radius r of a right circular cylinder with a fixed height of 48 inches is increasing. Find the…

A: topic - average rate of change of function

Q: The radius of a sphere increases at a rate of 3m/sec. Find the rate at which the surface area…

A: The surface area is

Q: The radius r of a right circular cylinder with a fixed height of 48 inches is increasing. Find the…

A: The formula of the volume of right circular cylinder is: V=πr2h Now, the height is fixed h=48. So V…

Q: The radius of a sphere increases at a rate of 3m/sec. Find the rate at which the surface area…

A: Rate of change of radius = 3m/s Find the change in surface area at radius = 6m

Q: The radius of a circle is increasing at a rate of 5 ft/min. At what rate is its area changing when…

A: We can find the rate of change of area as below.

Q: The area of a square with sides of length s is given by A = s2 . Find the rate of change of the area…

A: The area of a square with sides of length s is given by , A=s2. To find the rate of change of area…

Q: The altitude (,) of a right circular cylinder is always equal to the diameter (a) of the base. Find…

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Q: The radius r of a right circular cylinder with a fixed height of 48 inches is increasing. Find the…

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Q: The radius r of a circle is increasing at a rate of 9 centimeters per minute. Find the rate of…

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Q: Find the rate of change of the surface area of a hemisphere with respect to its radius. a. When the…

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Q: 18. If the radius of the circle increases at the rate of 0.01 cm per second, find the rate of change…

A: Topic:- Application of Derivative  Correct option = a

Q: The radius r of a sphere is increasing at a rate of 8 inches per minute. Find the rate of change of…

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Q: The radius of a balloon is increasing at the rate of 10cm/sec. At what rate is the surface area of…

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Q: Let A be the area of a circle with radius r that is increasing in size with respect to time. If the…

A: We have to find rate of change of the radius when radius is 6 cm and rate of change of area is given…

Q: The area of a circle is decreasing at a rate of 5 cm2/s. Find the rate of change of the circle’s…

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Q: The area of a square with sides of length s is given by A = s2. Find the rate of change of the area…

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Q: A heated circular plate has a radius of 24 in. What is the rate of change of the plate's radius if…

A: To find the rate of change of plate's radius

Q: The radius of a circle is increasing at a rate of 3 ft/min. At what rate is its area changing when…

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Q: The volume of a sphere is increasing at a rate of 8 cm3/sec. Find the rate of change of the radius…

A: Given : V= 32π/3 cm3              dV/dt = 8 cm3 /sec

Q: The radius r of a circle is increasing at a rate of 2 centimeters per minute. Find the rate of…

A: