How can you relate the rate of change for the surface area of a cube (dSA/dt) as compared with its volume (dV/dt) of the same side l?

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: Air is being pumped into a spherical balloon at a rate of 4.5 cubic feet per minute. Find the rate…

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Q: There is a water tower with a radius of 5 feet and a height of 30 feet. The water level is 25 feet…

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Q: find the rate at which the volume of a right circular cylinder of constant altitude 10 feet changes…

A: Given  Altitude=10feet We need to find the rate at which the volume of a right circular cylinder…

Q: The volume of a sphere is increasing at a rate of 4 cm3/sec. Find the rate of change of its surface…

A: We will use derivative as rate of change

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

A: given that a side of cubedecreases at a rate of 8m/sfind the rate at which the volume changes when…

Q: A cube is heated in such a way that the volume increases at a rate of 1 mm/s. The rate of change of…

A: A cube is heated in way that volume increases at the rate of 1mm/s. the side of the cube is 7mm…

Q: Water is dripping into a hemispherical bowl with a radius of 8 cm at a rate of 1 cubic cm per…

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Q: The volume of a sphere is.5 increasing at the rate of 3 cubic centimeters per second. Find the rate…

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Q: Is the rate of change of a cube's volume linearly proportional to the rate of change of its side?

A: Rate of change of volume of cube

Q: A cube’s surface area increases at the rate of 72 in2/sec. At what rate is the cube’s volume…

A: Given:

Q: 2): The side of a cube decreases at a rate of 6 m/sec. Find the rate at which the surface area of…

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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 edge of an expanding cube is changing at the rate of 2.3 cm/s at the instant its edge is 18.3 cm…

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Q: Find the rate of change of the area of a square with respect to the length z of a diagonal. What is…

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Q: A spherical snowball melts at a rate proportional to its surface area. Show that the rate of change…

A: Given that spherical snow ball melts at a rate proportional to its surface areaShow that rate of…

Q: If the rate of change of the surface area of a sphere with respect to its radius is 16pi sq cm, find…

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Q: Find the rate of change. Volume of a cube with respect to its sides when s = 5

A: The volume of a cube with side s is V=s3 Differentiate with respect to s dVds=ddss3=3s2

Q: What is the rate of change of the volumeof a ball (V = (4>3)pr3) with respect to the radius…

A: The volume of a ball with radius r is given by V=43πr3 Recall that the rate of change is given by…

Q: The temperature at a point in a ball with conductivity K is inversely proportional to the distance…

A: We know:

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: The radius of an bubble is increasing at the rate of 1/2 cm/s. At what rate is the volume of the…

A: Here  radius of bubble is given and rate of change of radius of bubble is also given

Q: side

A: Please refer to the image below

Q: The area of an equilateral triangle is decreasing at a rate of 4 sq. cm. per minute. Find the rate…

A: Given that  The area of an equilateral triangle is decreasing at a rate of 4 sq. cm. per minute.…

Q: The radius of a star(spherical) was r=a and was observed to increase by 0.01%. Use a linear…

A: Given data is : Radius(r) of a star (spherical) is increase by 0.01% To find the percentage of…

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 designer develops a cylindrical box with a fixed height of 15 cm. Calculate the instantaneous rate…

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Q: The linear density of a cable wire is the rate of change of its mass with respect to its length. A…

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Q: A cube is expanding at the rate of change 64 m³/s. What is the rate of change of its surface area…

A: This question is based on application of derivative.

Q: 2. The radius and lateral area of a right circular cylinder change at the rates of 1 cm/s and -2…

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Q: What is the average rate of change of the height of water in the vase with respect to the volume of…

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Q: Find the rate of change of volume of a sphere with respect to its surface area when the radius is 2…

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Q: Show that the rate of change of the area of a circle with respect to its radius is equal to the…

A: Our Aim is to show that the rate of change of area of a circle with respectto its radius is equal…

Q: The temperature at a point in a ball with conductivity K is inversely proportional to the distance…

A:

Q: A yellow balloon, spherical in shape is inflated with a rate of 100 cm3 /sec. Calculate the rate at…

A: Given

Q: The surface area of a cube is increasing at a rate of 15 square meters per hour. At a certain…

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Q: A right circular cylinder has a fixed height of 4 meters. Find the rate of change of its volume V…

A: Given: A right circular cylinder has a fixed height of 6 m.

Q: The radius of the sphere is decreasing at a rate of 2in/min. What is the rate of change of its…

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Q: 11. At what rate is the volume of the cube changing if the edge is 8 cm and is changing at 4 cm/s?

A: As we know that; The expression for the volume of the cube with the edge length ''a'' is: v=a3…

Q: A spherical balloon is deflated at a rate of 10 cm3 s-1. Find the rate change of the surface area…

A: given: A spherical balloon is deflated at a rate of 10 cm3s-1. we have to find the rate change of…

Q: A spherical balloon is being deflated at the rate of 10 cm/s. What is the rate of change for the…

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Q: Air is being pumped into a spherical balloon such that its radius increases at a rate of .50 in/min.…

A: r= 3 in dr = 0.5 in/min

Q: Find the rate of change. Volume V of a cylinder with respect to radius if the height is equal to the…

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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