A spherical balloon is inflated so that its radius increases at a rate of cm/sec. How fast is the volume of the balloon when the radius is 4 cm?

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

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

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

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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: 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 inflating at a rate of 277T in³/sec. How fast is the radius of the balloon…

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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…

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

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Q: A spherical balloon has a radius r that is increasing at a rate of 3 cm/s. At what rate is the…

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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: Water is poured into a conical tank 6 m across the top and 8 m deep at the rate of 10 m3min. How…

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

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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: A spherical snow ball is being made so that its volume is increasing at the rate of 8 ft /min. What…

A: given: dVdt=8 ft3 /min We have to find drdtwhen diameter of snowball is 4 ft i.e, radius= 2ft we…

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: 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…

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

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Q: 1. Water is flowing into a vertical cylindrical tank at the rate of 24 cu. ft. per min. If the…

A: Given , Water is flowing into vertical tank at rate if 24 cu .ft . per min. Radius of tank is 4ft.…

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

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

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

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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…

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Q: A spherical balloon is inflated so that its radius (r) increases at a rate of 1/3cm/sec. How fast is…

A: Vloume(V)=43πr3Differentiate w.r.t tdVdt=43π.3r2.drdt

Q: Air is pumped into a spherical balloon so that its volume increases at a rate of 100 cm /s. How fast…

A: d[r^n]/dr = n r^(n-1)

Q: a spherical balloon is filled with gas at a rate of 300 mm3/sec. Find the rate at which the surface…

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

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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: How fast is the volume of a cube changing when the edge is 15 cm if the edge is changing at the rate…

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Q: ) A snowball is melting at a rate of 1 cm3 per second. If it remains spherical, how fast is the…

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Q: The radius of a sphere, initially zero, increases at the rate of 6ft per sec. Find how fast the…

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Q: A paper cup has the shape of a cone with height 10 cm and radius 3 cm (at the top). If water is…

A: From the given problem the representative diagram is shown as below: Let the radius of the cone be…

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 5m is being filled with water at a rate of 4 m^3/min. How fast is the…

A: Given:         radius of cylinder (r)=5m         rate of water filled dvdt=4m3/minwe know that…

Q: A conical glass whose radius is 5m and altitude 12m is being filled at the rate of 10 cu. m/sec. How…

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

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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: A spherical balloon has a radius r that is increasing at a rate of 3 emfs. At what rate is the…

A: Given: drdt=3πcm/s   To find: dvdt when r=10

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

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Exponential Growth Model

The relation that represents an exponential function is: