Imagine a sphere whose radius r increases at a rate of 3 cm/s. At what rate is the volume V of the sphere increasing when r = 10 cm?

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Q: The side of a cube increases at the rate of 11 m/sec. Find the rate at which the volume of the cube…

A: givenside of cube(a)=5mdadt=11m/secVolume of cube (v)=a3differentiating with respect to…

Q: The legs of an isosceles right triangle increase in length at a rate of 2 m/s. a. At what rate is…

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Q: The base radius, r, of a cylinder is decreasing at a rate of 0,2cm/s while its height, h, is…

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Q: The side of a cube is increasing at a rate of 5cm/sec, find the related change in surface area wher…

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Q: The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is…

A: Given that, drdt=1.1 in/s and dhdt=-2.7 in/s. Also, it is given that r=102 in. and h=162 in. It is…

Q: The radius of a right circular cone is increasing at a rate of 1.2 in/s while its height is…

A: Differentiate volume wrt t

Q: Gas is being pumped into a spherical balloon at the rate of 10 cubic inches per second. When the…

A: we have given that Gas is being pumped into a spherical balloon at the rate of 10 cubicinches per…

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: The ice cream in a sugar cone (conically shaped) has all melted and is dripping out a hole in the…

A: To express r in terms of h, use the the ratio between the height and radius of the cone is constant…

Q: Water is being pumped (at a constant rate of 7 ft3 per minute) into an upside-down circular cone…

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Q: A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius…

A: Rate of Radius of outer ripple increasing = 1 ft/sec                    Radius = 4 feet

Q: Find the rate of change of the volume of a cone with a constant height of 5 m with respect to radius…

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Q: The surface area of a sphere increases at a rate of 87 m/sec. Then the rate at which the radius…

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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: A spherical balloon has a radius r that is increasing at a rate of 3 cm/s. At what rate is the…

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Q: Suppose the radius of a sphere is increasing at a rate of 5 in/second.  At what rate is the surface…

A: Given that radius of a sphere is increasing at an of 5 in/sec. Let r be the initial radius of the…

Q: The surface area of a sphere increases at a rate of 90 m/sec. Then the rate at which the radius…

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Q: A spherical balloon is being deflated at a rate of 80 cm³/min. At what rate is the radius decreasir…

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Q: The surface area of a sphere increases at a rate of 55 m²/sec. Then the rate at which the radius…

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Q: A spherical snow ball is being made so that its volume is increasing at the rate of 8 ft /min. What…

A: given: dVdt=8 ft3 /min We have to find drdtwhen diameter of snowball is 4 ft i.e, radius= 2ft we…

Q: Consider a pool shaped like the bottom half of a sphere, that is being filled. The radius of the…

A: The volume of hemisphere filled with liquid to height h = πrh2-π3h3

Q: The surface area of a sphere increases at a rate of 64 m²/ sec. Then the rate at which the radius…

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Q: If the original 24 m edge length x of a cube decreases at the rate of 5 m/min, when x = 3 m at what…

A: (a)Given:

Q: Find the rate of change of the total surface area of a cylinder of radius r and height h, when the…

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Q: side

A: Please refer to the image below

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: The legs of an isosceles right triangle increase in length at a rate of 5 m/s. a. At what rate is…

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Q: The radius of a right circular cone is increasing at a rate of 1.2 in/s while its height is…

A: To calculate the required rate of change using partial derivatives

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 volume of a cube decreases at a rate of 12.1 m/sec. Find the rate at which the side of the cube…

A: we have to find the rate change of a side of cube

Q: Find the surface area of a sphere at the instant when the rate of increase of the volume of the…

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Q: a water tank has the shape of an inverted circular cone with a base radius of 2m and a height of 4m.…

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Q: 15. Gas is being pumped into a spherical balloon at the rate of 10 cubic inches per second. When the…

A: NOTE: Refresh your page if you can't see any equations. . here we have the diameter is 30 inches so…

Q: A Fluid flows in an inverted conical tank, 14 in diameter on top and 24in deep at a rate of…

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Q: A pebble is dropped into a calm pond, causing ripples in the form of concentric circles, as shown.…

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Q: The volume of a sphere is increasing at a rate of 40 cm^3/sec. At what rate is the radius ofthe…

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Q: The radius r of a sphere is increasing at a rate of 4 inches per minute.

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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 snowball is melting at a rate of 1 cm3 per second. If it remains spherical, how fast is the…

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Q: 15. Water is being poured at the rate of 150 cm³/s into an inverted cone with a diameter of 3 meters…

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Q: The surface area of a sphere increases at a rate of 52 m²/sec. Then the rate at which the radius…

A: The surface area of sphere is given by A=4πr2

Q: A conical glass whose radius is 5m and altitude 12m is being filled at the rate of 10 cu. m/sec. How…

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Q: The radius of a sphere decreases at a rate of 4 m/s. when the radius is 7 m, then the rate at which…

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Q: A spherical balloon has a radius r that is increasing at a rate of 3 emfs. At what rate is the…

A: Given: drdt=3πcm/s   To find: dvdt when r=10

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

A: Given that volume of a cube is increasing at the rate of 8cm3/sec find out the fastness in the…