A spherical balloon is being inflated. When the radius of the balloon is 15 centim ters, air is being pumped in at a rate of 3 cubic centimeters per second. At this moment, what rate is the radius is the balloon changing? Include units. (The volume of a sphere radius r is Tr³. You may not assume that air is being pumped in at a constant rate.)

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Q: . Find the rate at which the volume increases when the radius is 30 cm. (Hint: Volume 4 of the…

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Q: The volume of a spherical balloon changes with respect to the radius r. At what rate (in ft°/ft)…

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A: Given

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A: We will find the rate of change of volume of sphere at a given radius.

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A: let side of cube is x then rate at which side increase is 5 m/secie.  dxdt=5 m/sec

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A: Given rate of increase in the surface of sphere=64m2/sec And radius of sphere=3m Now we have to find…

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A: We have given, Y= (x-2)0.5 Y=0 Y=1 X=2   We know if the radius and height of a cone are r unit and h…

Q: The volume of the sphere is increasing at the rate of 6cm^3/hr. At what rate is its surface area…

A: Given that the volume of the sphere is increasing at the rate of 6  cm^3/hr. We have to find the…

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Q: The side of a cube increases at the rate of 7 m/sec. The rate at which the volume of the cube…

A: Given the side of a cube increases at a rate of = 7 m/sec. and the final rate of change of volume…

Q: The side of a cube decreases at a rate of 9 m/sec. Find the rate at which the volume changes, when…

A: If the rate is decreasing then it will be the negative.

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Q: The radius of a sphere increases at a rate of 4m/sec. Find the rate at which the surface area…

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Q: The surface area of a sphere increases at a rate of 77 m2/sec. Then the rate at which the radius…

A:

Q: The surface area of a sphere increases at a rate of 59 m?/sec. Then the rate at which the radius…

A: We have to find rate of change of radius

Q: If the radius of a sphere increases at a rate of 0.5 m/sec, then the rate at which the volume of the…

A: Find the rate at which volume of a sphere increase s

Q: The volume of the sphere is increasing at the rate of 6 cm?/hr. At what rate is its surface area…

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Q: The volume of a sphere is increasing at the rate of 6 cm3/hr. at what rate is its surface area…

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Q: The side of a cube decreases at a rate of 7 m/sec. Find the rate at which the volume changes, when…

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Q: If the radius of a sphere increases at a rate of 1.5 m/sec, then the rate at which the volume of the…

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Q: The conical tank shown here is filled with olive oil weighing 49 lb/ft?. How much work does it take…

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A: Given that the shape of the crater of a volcano is right circular cone  Whose diameter , d = 1 mile…

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A: Base(top) to height relation where 0≤x≤3 and 0≤y≤3 x=y So the rate volume is, ΔV = 8xΔy ΔV = 8yΔy…

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Q: The surface area of a sphere increases at a rate of 84 m2/sec. Then the rate at which the radius…

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Q: The radius of a sphere increases at a rate of 6m/sec, then the rate at which the volume increases…

A: Let's find.

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A: Let r is the radius of the sphere . S is the surface area of the sphere. we know that…

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A:

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

A: Use the formula for volume of cube and take its derivative than substitute the given values.

Q: The side of a cube decreases at a rate of 8 m/sec. Find the rate at which the volume changes, when…

A: Volume of the cube =side^3 If side decreased  then volume also decreased

Q: The side of a cube decreases at a rate of 9 m/sec. Find the rate at which the volume changes, when…

A: Topic- Application of Derivative

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A: Given: A reservoir shaped like a right-circular cone, point down, 20 ft across the top and 8 ft…

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Q: A cylinder has a base radius of 6ft and a height of 18ft. What is its volume in cubic ft, to the…

A: Given thatBase radius  r = 6 ft.height            h = 18 ft.volume of the cylinder is given byV =…

Q: The surface area of a sphere increases at a rate of 77 m2/ sec. Then the rate at which the radius…

A:

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

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A: Snowball represents a sphere So , Surface Area of sphere is 4πr2.  And , d=2r.  Using this we solve…

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

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Q: The surface area of a sphere increases at a rate of 95 m2/ sec. Then the rate at which the radius…

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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: Let A is the surface area of Sphere.

Q: The surface area of a sphere increases at a rate of 82 m² / sec. Then the rate at which the radius…

A: Use rate of change

Q: An aluminum can is to be constructed to contain 2500 cm^3 of liquid. Let r and h be the radius of…

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

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Q: A cocktail glass with a bowl shaped like a hemisphere with diameter 8 cm contains a spherical cherry…

A: Given that, x2+(y-4)2=42 x2=16-(y-4)2 x=16-y-42 From the washer method,…