a cylinder has a height equal to its radius. find the rate of change of volume with respect to radius.

Q: A spherical balloon is inflated and its volume increases at a rate of 30 in3 /min. (a). What is the…

A: Given that, The spherical balloon is inflated and its rate of change of volume is; dVdt=30 (in3min)…

Q: the velocity of a particle is the rate of change in the position function over time true or false

A: We have to check

Q: If a snowball melts so that its surface area decreases at a rate of 1cm /min, find the rate at which…

A: Diameter= DRadius = r =D/2Surface area = A= 4pi*r^2Given dA/dt= -1 cm^2/min (negative because…

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

A:

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

A:

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: Find the rate of change. The diameter of a circle with respect to radius

A:

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 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: Find the rate at which the surface area of the water changes when the water is 10 ft high if the…

A:

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

A:

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 spherical snowball is melting in such a way that its volume is decreasing at a rate of 2 cm / min.…

A: Given-  dVdt=-2cm3/min (negative sign indicates that it is decreasing). To find- The rate of radius…

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

A:

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

A:

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 volume of a different sphere is increasing at a rate of 24 cubic inches per minutes and the…

A:

Q: A cone-shaped tank of water is leaking water at a constant rate of 3 m³/hour. If the base radius of…

A: Using volume  of cone and applications of derivative idea we solve this

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: 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…

A:

Q: If the rate of change in volume of a sphere is equal to its rate of change of its radius. What is…

A: if we let the radius of square = r unit then volume of the square =4/3 πr3 unit3

Q: The radius of a sphere decreases at a rate of 3 meters per second. Find the rate at which the…

A:

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 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…

A:

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

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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 time rate of change of the radius of a sphere is 1/2π, when its radius is 5 cm , find the rate…

A: According to the question, we have to find the rate of change of surface area of the sphere with…

Q: If the radius of a cone increases at a rate of 36 inches per second and the height decreases 2 feet…

A: Given

Q: The height h of a right circular cylinder is twice its radius r. Find the rate of the volume V of…

A: The volume of the right circular cylinder is given as: V=πr2h where 'r' is the radius of the cone…

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

A:

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

A:

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: The rate of change of the area enclosed between the circle and the square is square meters per…

A:

Q: The radius of a right circular cone is increasing at 3 cm/min whereas the height of the cone is…

A:

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: A plane flying horizonrally at an altitude of 1 mi and a speed of 500 mi/h passes directly over a…

A: given that plane is flying horizontally at an altitude of 1mi speed=500 mi/h find the rate at which…

Q: a. If a snowball melts so that its surface area decreases at a rate of 1 cm²/min, find the rate at…

A:

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

A:

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: A triangle has a base that is decreasing at a rate of 4 cm/s with the height being held constant.…

A: Let b and h be the base and height of the trianglegiven rate at which base is decreasing, dbdt=4cm/s…

Q: 2. The height and volume of a right circular cone change at the rates of 1 cm/s and -2 cm^3/s,…

A: Let's find.

Q: The radius of a right circulare cylinder is increasing at the rate of 3 in/sec, while the height is…

A: To determine the change of rate of the volume of cylinder.

Q: Amedeo Avogadro discovered the relationship between the pressure and the volume of a gas. O True…

A: Answer

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

A:

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

A: Let h and r denote the hieght and radius of base of the cylinder.1