Air is escaping from a spherical balloon at the rate of 2cm per minute. How fast is the radius shrinking when the volume is 367 cm³?

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 cylindrical tank with radius 6 m is being filled with water at a rate of 3 m³/min. How fast is the…

A:

Q: The edges of a cube are expanding at a rate of 5cm per second. How fast is the volume changing when…

A:

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: A Ferris wheel with a radius of 10 m is rotating at a rate of one revolution every 2 minutes. How…

A: the height is given byh = 10 sin (pi * t) + 10dh/dt = 10 cos (pi * t) * pi

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

A:

Q: Water is flowing at the rate of 9 ft3/min into a tank that is in the shape of a right circular…

A: Let r be the radius of base of cylinder, then r=2 ft .Let h be the height of water level at any time…

Q: Suppose the sides of a cube are expanding at a rate of 2 inches per minute, How fast is the volume…

A:

Q: Water is being poured at the rate of 27 m³/min. into an inverted conical tank that is 12-meter deep…

A: Given that a canonical tank that had radius is 6meter and height is 12 meter and dh/dt= 1/6…

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: 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: Liquid is escaping from a conical funnel at the rate of 3 cm3 /min. If the top of the funnel has a…

A: Given, r= 4 cm h= 20 cm dV/dt= 3 cm³/min Therefore, r/h= 4/20= 1/5 r= h/5

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 cylindrical tank with radius 5 m is being filled with water at a rate of 2 m3/min. How fast is the…

A:

Q: Water runs into a sunken concrete hemi- spherical bowl of radius 5 m at the rate of 0.2 m3/sec. How…

A: The derivative gives the rate of change of some variable with respect to other quantity. If a…

Q: The radius of a spherical balloon is increasing at the rate of 2 cm per minute. How fast is the…

A: Let r be the radius of spherical ballon

Q: A cylindrical tank with radius 3 m is being filled with water at a rate of 4 m³/min. How fast is the…

A: Given : The radius of the cylindrical tank is 3 m. Water is filled at a rate of 4 m3/min

Q: Water is flowing at the rate of 6 ft/min into a tank that is in the shape of a right circular…

A: Given data:   The rate at which water is flowing in the cylindrical tank is dV/dt =6 ft3/min. 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 rectangle is expanding such that its length is always 4 times its width. If the width is…

A:

Q: Water is being poured at the rate of 27 m²/min. into an inverted conical tank that is 12-meter deep…

A:

Q: Water is flowing into a vertical cylindrical tank at the rate of 5cu.ft/min. if the radius of the…

A: The volume of a cylinder:,V = πr2hWhere, V = Volume of the cylinder  r = Radius of the base  h =…

Q: A cylindrical tank with radius 8 m is being filled with water at a rate of 3 m3/min. How fast is the…

A: It is known that the volume of the cylinder is V=πr2h where r is radius and h is height. Given that…

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: All the edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the volume…

A:

Q: A spherical balloon is increasing in volume at 24t Cm . How fast is the radius ст S. of the balloon…

A:

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: 2. A cylindrical plastic container with a radius of 15 cm is being filled with orange juice at a…

A:

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: A spherical balloon is inflated so that its radius increases at a rate of cm/sec. How fast is the…

A: Volume of the sphere is given by:  V = 43πr3

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: The volume of a cube is increasing at the rate of 6 cm/min. How fast is the surface area increasing…

A: It is given that, the volume of a cube is increasing at the rate of 6 cm3/min.   The objective is to…

Q: A cylindrical tank with radius 5 m is being filled with water at a rate of 2 m3/min. How fast is the…

A:

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

A:

Q: The radius of a sphere is increasing at a rate of 4 meters per minute. When the radius is 11 meters,…

A:

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: A cylindrical tank with radius 6 m is being filled with water at a rate of 4 m3/min. How fast is the…

A: From the given information it is given that:Radius of cylindrical tank(r) = 6mRate at which the…

Q: a cylindrical tank with radius 7 m is being filled with water at a rate of 2 m3/ min how fast is the…

A:

Q: A comment loses material when it gets close to the sun at a rate of 100 m³ per minute. Assuming that…

A: Given a comet loses material when it gets close to the sun at a rate of 100 m³ per minute.

Q: A cylindrical tank with radius 5 m is being filled with water at a rate of 3 cu. m / min How fast is…

A: Given, Radius of the cylindrical tank = 5 m Water rate = 3 m3/min

Q: coffee is draining out of a conical filter at a rate of 2.25 inches cubed per minute. If the cone is…

A: given: coffee is draining out of a conical filter at a rate of 2.25 inches cubed per minute. If the…

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: 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…

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.