A spherical balloon is being inflated. The volume is increasing at a rate of 5 mm per second. How fast is the radius changing when the diameter is 8mm?

Q: Suppose the radius of a sphere are expanding at a rate of 6 inches per minute. How fast is the…

A: Let us suppose the radius of sphere be R. Given that :   dRdt=6 incheminute.  Radius=Diameter2=122=6…

Q: A spherical balloon is being filled with air at the constant rate of (2 cm3)/(sec). How fast is the…

A: Given that  A spherical balloon is being filled with air at the constant rate of (2 cm3)/(sec). This…

Q: a. Air is being pumped into a spherical ball in such a way that the volume increases at a rate of 10…

A: Given: Volume of sphere is increasing at a rate of 10 cm^3/sec.

Q: All edges of a cube are expanding at a rate of 9 centimeters per second. (a) How fast is the volume…

A: GivenAll edges of a cube are expanding at a rate of 9 centimeters per second

Q: Water is injected into a ball-shaped container of radius RR at a rate of 2 cm^3 per second. How fast…

A: Radius of spherical ball is R. Rate change in volume is 2 cubic centimeters. Mathematically, dVdt=2…

Q: Sugar is poured into a conical tank at the rate of 15cm3/sec whose bottom radius is always quarter…

A: The volume of a cone is given by the formula V=13πr2h. Where, V-volume, r-radius and h is the height…

Q: A spherical balloon is being filled with air at a constant rate of 3 cm3/s. How fast is the radius…

A: Let,Volume of sphere = VRadius of sphere = rRate at which the volume of sphere is increasing = dVdt…

Q: A stone dropped into a still pond sends out a circular ripple whose enclosed area increases at a…

A:

Q: Each side of a square is 6 ft and is increasing at a rate of 2 ft per second. How fast is the area…

A: By differentiating equation of area of square with respect to time and substituting the value of…

Q: The radius of a sphere is increasing at a rate of 3 mm/s. How fast is the volume increasing when the…

A:

Q: The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when the…

A: Given that the diameter= 100 mm So the radius is=r=1002=50 mm Given that the radius of a sphere is…

Q: A spherical balloon is inflated with gas at a rate of 10 cubic metres per minute. How fast is the…

A:

Q: The radius of a sphere is increasing at a rate of 4mm/s. How fast is the volume increasing when the…

A: The rate of change of the radius of the sphere, drdt = 4 mm/s To evaluate : The rate at which the…

Q: Air is escaping from a spherical balloon at the rate of 2cm per minute. How fast is the radius…

A: V=43πr3

Q: The volume of  a cube is increasing at a rate of 9 feet3/sec . how fast is the surface area…

A:

Q: A spherical balloon is being deflated at a rate of 80 cm3/min. At what rate is the radius decreasing…

A:

Q: As a circular metal griddle is being heated, its diameter changes at a rate of 0.01 cm/min. Find the…

A:

Q: Air is being pumped into a sperical balloon so that its volume increases at a 12. rate of 16 cubic…

A:

Q: A spherical balloon is being inflated at a rate of 20 cubic centime- ters of air per second. How…

A: We will use chain rule and the information provided.

Q: A spherical balloon is inflated so that its volume is increasing at the rate of 7 ft^3/min. How fast…

A: given: A spherical balloon is inflated so that its volume is increasing at the rate of 7 ft^3/min.…

Q: The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing when the…

A: Let be the volume and r be the radius of the sphere respectively.

Q: The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the…

A: Volume of sphere= =43πR3 where R is the Radius of the sphere.

Q: A snowball is melting at a rate of 2.4ft^3 hr^-1 – if the snowball remains a sphere throughout the…

A: given: A snowball is melting at a rate of 2.4ft3/hr. that implies dVdt=-2.4ft3/hr where V is the…

Q: A cylindrical tank with radius 3 m is being filled with water at a rate of 3 m³/min. How fast is the…

A:

Q: A conical reservoir is losing water at the rate of 12 cubic feet per minute. If the radius is % the…

A: Let the height of the conical reservoir be h. Then the radius will be = h/4 Therefore we get the…

Q: The volume of a cube is increasing at a rate of 9 cubic centimeters per second .How fast is the…

A: Solution:-

Q: Air is being pumped into a spherical balloon so that it volume increases at a rate of 100 cubic cm /…

A:

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: The radius of a sphere is increasing at a rate of 4 mm /s. How fast is the volumeincreasing when the…

A:

Q: A spherical party balloon is being inflated with helium pumped in a rate of 7 cubic feet per minute.…

A: Given,           A spherical party balloon is being inflated with helium pumped in a rate of 7 cubic…

Q: The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the…

A:

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: All edges of a cube are expanding at a rate of 7 cm per second. How fast is the surface area…

A: Given that all edges of a cube are expanding at a rate of 7 cm per second. Let the edge of a sphere…

Q: at a certain instant, the dimensions of a rectangle are 8 and 12 feet and they are inreasing at the…

A:

Q: A cone with an altitude of 50 cm has its base radius changing at the rate of one millimeter per…

A:

Q: A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 2…

A: Given ,  A stone dropped in a pond sends out a circular ripple whose radius increases at a constant…

Q: Suppose the radius of a sphere is expanding at a rate of 3 inches per minute. How fast is the volume…

A: Let V & r be the volume and radius of the sphere at any time t respectively. Given that, the…

Q: A 13-ft ladder is leaning against a house when itsbase starts to slide away. By the time thebase is…

A: If a ladder is leaning against a wall and when its base starts to slide away it makes a triangle…

Q: A rectangle has a length of 7 inches and a width of 8 inches, whose sides are changing. The length…

A: Given: A rectangle has a length of 7 inches and a width of 8 inches, whose sides are changing.The…

Q: as a balloon in the shape of a sphere is being blown up, the volume is increasing at the rate of 4…

A: Volume of the sphere Shape ballon: V = 4/3ℼr3   (r = radius)   Now differentiate with respect to L,…

Q: A comet loses material when it gets close to the Sun at a rate of 100 cubic meters per minute.…

A: Given Comet is a sphere Its radius is 200 meters Let V be the volume of the comet then r be the…

Q: how

A:

Q: A spherical balloon is being filled with air at the constant rate of 2 cm³ How fast is the radius…

A: Given that The spherical balloon is being filled with air at constant rate of 2cm3/sec. Since the…

Q: The spherical balloon is being filled with air at the constant rate of ( 2cm3  ) / (sec). How fast…

A: Given: The spherical balloon is being filled with air at the constant rate of 2cm3/sec We know that,…

Q: The Volume of a cube is increasing at the rate of 8 cm3/sec.How fast is the surface area increasing…

A: Given that volume of a cube is increasing at the rate of 8cm3/sec find out the fastness in the…

Q: Air is being pumped into a spherical balloon so that its volume increases at a rate of 50 cm3/s. How…

A: Let radius of the balloon is =r and diameter =d=30 cm It is given that Volume increases at rate…

Q: Helium is pumped into a spherical balloon at a constant rate of 3 cubic feet per second. How fast is…

A:

Q: The radius of a sphere is increasing at a rate of 4mm/s.How fast is the volume increasing when the…

A: Given that the radius of a sphere is increasing at a rate of 4mm/s. That is, Now consider the…

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.