A spherical snowball melts at a rate proportional to its surface area. Show that the rate of change of the radius is constant. (hint: surface area: 4(pi)r^2)

Q: outer ripple is increasing at a constant rate of 2 feet per second. When the radius is 10 at rate is…

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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: What is the rate of change of the areaof a circle (A = pr2) with respect to the radius when the…

A: To find the rate of change of the area of a circle with respect to the radius when the radius is…

Q: An oil slick on a lake is surrounded by a floating circular containment boom. As the boom is pulled…

A:

Q: A cylinder has a height equal to its radius. Find the rate of change of volume V with respect to…

A: volume of cyclinder v =pi r2 h --1 given height =radius  h=r

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…

A:

Q: The radius of a spherical balloon is increasing at the rate of 0.8 cm / minute. How fast is the…

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Q: Air is being pumped into a spherical balloon at a rate of 5 cubic centimeters per minute. Determine…

A: Given : The air is pumped into a balloon at a rate of 5 cm3/min The diameter of the balloon is 20 cm

Q: the radius of a circle is increasing at a constant rate of 100 meters per second. at what rate is…

A: First of all, consider the area for the circle.Then differentiate on both sides of equation w.r.t…

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: 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: An ice cube is growing 0.2cm per minute. Find rate surface area changes when length is 8cm

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

A: It is given that, the spherical snowball melts at a rate proportional to it’s surface area. This can…

Q: A large weather balloon is being inflated with air at the rate of 0.9 ft3 per minute. Find the rate…

A: Given a large weather balloon is being inflated with air at the rate of 0.9 ft3 per minute. Volume…

Q: A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 4 ft/min.…

A: Area of a circle of radius r is given by  A = πr2                ...(1) Differentiate with respect…

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 pebble is dropped into a calm pond causing ripples in the form of concentric circles. The radius r…

A:

Q: a snowball melts so that its surface area decreases at a rate of3 cm¯/min, find the rate atwhich th…

A: Surface Area of a spherical ball is  A=4πr2 where 'r' is the radius of the ball.

Q: A thin sheet of ice is in the form of a circle. If the ice is melting in such a way that the area of…

A:

Q: A piston is seated at the top of a cylindrical chamber with radius 5 cm when it starts moving into…

A: Let h be the distance between the piston and base of the chamber.

Q: An oil tanker aground on a reef is forming a circular oil slick about 0.1 foot thick. If the oil was…

A: Given that  An oil tanker aground on a reef is forming a circular oil slick about 0.1 foot thick. If…

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

A:

Q: The volume of a sphere is changing at a constant rate. Show that the surface area changes at a rate…

A:

Q: An ice cube in a freezer is growing due to accretion, each edge is increasing by 0.2 cm per minute.…

A:

Q: A spherical balloon is inflated with gas at the rateof 800 cubic centimeters per minute. (b) Explain…

A: To find the rate of change of the radius, differentiate the volume of the sphere, V=43πr2 with…

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: The radius of a circle is increasing at the rate of 0.7 cm/sec.what is the rate of increase of its…

A: The radius of a circle is increasing at the rate drdt= 0.7 cm/sec r = radius of the circle

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: The radius of a circle is increasing at a rate of 5 centimeters per minute. Find the rate of change…

A: We can find the answer as below using the given data.

Q: gas is escaping a spherical ballon at the rate of 4cm per minute . how fast is the surface area…

A: Given that, Gas is escaping a spherical balloon at the rate of 4 cm per minute. The objective is to…

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

A:

Q: Air is pumped into a spherical balloon at the constant rate of 200 cubic centimeters per second. How…

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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: spherical balloon is inflated with gas at a rate of 900 cubic centimeters per minute.

A: Volume of the sphere is V=43πr3where r = radius of the sphere

Q: A circle has an initial radius of 50 ft when the radius begins decreasing at a rate of 2 ft>min.…

A: Let r be the radius of the circle.The initial radius is given by r = 50 ft.Given that, the radius…

Q: ow fast is the radius changing when the diameter of the balloon is 50 cm?

A: Given: A spherical balloon is inflated at a rate of 1000 cm3 /sec . Diameter of the balloon = 50 cm

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

A: Given

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

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 spherical droplet of water evaporates at a rate of 1 mm3/minute. Find the rate of change of the…

A:

Q: A bacterial cell is spherical in shape. If the radius of the cell is increasing at the rate of 0.01…

A: Volume of sphere: V = 43πr3, where r is radius of sphere. Surface area of sphere: S = 4πr2, where r…

Q: Air is being pumped into a spherical balloon at a rate of 4 cm3/min. Determine the rate at which the…

A:

Q: A spherical balloon is being inflated at the rate of 12m /min. If the radius of the balloon is 6m,…

A:

Q: How can you relate the rate of change for the surface area of a cube (dSA/dt) as compared with its…

A: we know that surface areaS.A. and volumeV of cube is given by S.A.=6l2…

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

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.