The surface area of a sphere increases at a rate of 90 m2/sec. Then the rate at which the radius changes, when the radius is 5 m is. O 0.95 m/sec O 2.86 m/sec O 1.43 m/sec O 0.72 m/sec O 1.15 m/sec

Q: The density of a type of stone is 2000 kg/m^3. Find the work needed to build a stone cone with a…

A: Given: The density of the stone is 2000 kg/m3. The radius of the stone cone, r = 100m. And, the…

Q: A cylindrical water tank 6 meters high with a radius of 2 meters is buried so that the top of the…

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Q: A manufacturing firm wants to package its product in a cylindrical container 1 ft. high with surface…

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

A: Given the radius of a sphere changes increases at the rate of 3 m/sec. To find the rate at which…

Q: The lateral area L of any prism whose altitude measures h and whose base has perimeter P is given by…

A:

Q: The surface area of a sphere increases at a rate of 59 m2/ sec. Then the rate at which the radius…

A: Surface area of sphere, S = 4(pi)r^2 Where, r= radius of sphere

Q: The volume V = (4/3)πr3 of a sphericalballoon changes with the radius.By approximately how much does…

A: To find the rate at which the volume changes, you must find the derivative of the volume function.…

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Q: A right cylindrical tank has a height of 12 meters and a radius of 3 meters. Carter fills this tank…

A: Given data, Height of right cylindrical tank, h = 12 m Radius of right cylindrical tank, r = 3 m…

Q: |Find the average distance from the origin over all the points in the unit circular disk 2² +y? <1.…

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

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

Q: 2, The hadiusS r of a sphere is increasing as a vate af 3amimin. Find the rate af Ghane e Of Ahe…

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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 surface area of a sphere increases at a rate of 66 m2/sec. Then the rate at which the radius…

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Q: The total surface" area, S, of a cone of base radius, r, and perpendicular height, h, is given by S…

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Q: The radius length of the base of a right circular cylinder is 6 in. The height of the cylinder is 10…

A: a) The formula of the lateral area of the right circular cylinder is, AL=2πrh where r is radius and…

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: A conical tank with a diameter of 2 m across the top and 3 m high is filled with water. Find the…

A: The given problem is solved below in detail.

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: 2. Let V be the volume of a right circular cone of height 10 whose base is a circle of radius 4…

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Q: The cylindrical tank shown in the accompanying figure is filled with a liquid weighing 50 lb/ft³.…

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Q: Find the volume of liquid needed to fill a sphere of radius R to height h (Figure 19). FIGURE 19…

A: Assume the horizontal distance between the surface of the sphere and the height h is x.

Q: The radius of a sphere increases at a rate of 2m/sec. Find the rate at which the surface area…

A: In sphere Rate of radius= 2m/s Find the rate of change in surface area?

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: Water pours into a conical tank of height 10 meters and radius 4 meters at a rate of 6m /min. 1…

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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…

A: Solve it

Q: Find the area of the adjacent surface of a triangular prism whose base is a triangle with sides a =…

A: Area is the measure of space occupied by a flat surface. It is measured in terms of the number of…

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

A: Let the side of the cube be a m Then, given dadt=-7m/sec    (- sign indicates side is decreasing) To…

Q: The temperature (in degrees centigrade) at a point P on a circular wire of radius 2 cm centered at…

A: Given: The temperaturein Co at a point P on a circular wire of radius 2cm at the originis equal to…

Q: A can of tennis balls is twelve inches high and has a diameter of four inches. The can holds three…

A: Volume left between can and tenis balls =  Volume of cylinder - volume of 3 balls.

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.

Q: Find volume by evaluating vating triple integralspherical cordinates) use dp dodo Sin o

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Q: The radius of a sphere increases at a rate of 2m/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 57 m2/sec. Then the rate at which the radius…

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

Q: The volume V = (4/3)πr3 of a sphericalballoon changes with the radius.At what rate (ft3/ft) does the…

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: A water heater that has the shape of a right circular cylindrical e tank with a radius of 1 ft and a…

A: Given : radius = 1 ft  Height = 4 ft

Q: A spacecraft has landed on a strange flat object and has measured its density (103kg /m3) at several…

A: Given, Density= 103 kg/m3  Thickness= 1.4 m Area=3500 m2

Q: a very large cylindrical-shaped tank has a radius of 4 feet and a height of 15 feet. The tank is…

A: Given problem is : a very large cylindrical-shaped tank has a radius of 4 feet and a height of 15…

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

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

A: Use the concept of derivative and apply this on formula of surface area of sphere.

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

A: Surface area of sphere is S= 4πr^2. And rate of change means derivatives.

Q: A cylindrical water tank 8 meters high with a radius of 2 meters is buried so that the top of the…

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

Q: A cylindrical water tank meters high with a radius of 2 meters is buried so that the top of the tank…

A: Given:       Radius of layer r=2 m  weight water =9800 N per cubic meter  Volume v=πr2∆y…

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

A:

Q: A full water tank in the shape of an inverted right circular cone is 8 m across the top and 4 m…

A: Draw the figure according o given information, which is given below. Here, diameter D= 8 m Hence,…

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