A spherical balloon is increasing in volume at 24t Cm . How fast is the radius ст S. of the balloon increasing when the radius is 6 cm?

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: 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: The volume of a right circular cylinder is 60 cm3 and is increasing at 2 cm3/min at a time when the…

A: First we have to differentiate expression of volume with respect to time.

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 spherical balloon is inflating with helium at a rate of 192n ft° / min. How fast is the balloon's…

A: V=43πr3S=4πr2

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 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: Two concentric circles are expanding, the outer radius at the rate of 5 ft/sec and the inner one at…

A: Let A1 and A2 be the areas of the inner and outer circles at any instant and 'A' be the area between…

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: Air is being pumped into a spherical balloon so that its surface area increases at a ate of 100…

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: Water is pumped into a cylindrical tank which is 5m/tall, and has a radius of 1m (with the flat…

A: Given, Height of the cylindrical tank is 5 m. Radius of the cylindrical tank is 1 m. Water is pumped…

Q: m Oil is running into an inverted conical tank at the rate of 37 -. If the min tank has a radius 2.5…

A:

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 cylindrical tank of radius 10 feet is being filled with wheat at the rate of 314 cubic feet per…

A: consider the radius of a cylindrical tank by r. The volume of a cylindrical tank is given as V. The…

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

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

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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: 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: 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: A cylinder of radius 5 cm and height 10 cm is lowered (circular face first) at a rate of 1 cm/sec…

A: To find: The rate at which the water lavel rising at the instant the cone is completely submerged.

Q: A cylindrical tank with radius 6 m is being filled with water at a rate of 2 m/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: 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: A Helium is being pumped into a spherical balloon at a rate of 12cm³/min. Determine the rate at…

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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: 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: 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 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: The two equal sides of an isosceles triangle with fixed base b are b are decreasing at the rate of 3…

A: Solution :-

Q: Water is pouring into a conical vessel 15 cm deep and having a radius of 3.5 cm across the top. If…

A: Given the water is pouring into a conical vessel of 15 cm deep and the radius of 3.5 cm across the…

Q: A liquid is flowing into a vertical cylindrical tabk of radius 6 ft at the rate of 8 ft³/min. How…

A: r=6 ft  &  dVdt=8 ft3min,  where r is the radius, V is the volume at any time t. Let h 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: 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: Air is being pumped into a spherical balloon at a rate of 4 cm3/min. Determine the rate at which 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 spherical balloon is being inflated at the rate of 12m /min. If the radius of the balloon is 6m,…

A:

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

A: Given , Bacterial cell is in spherical shape.Let radius be 'r' μm . ∴ Volume of cell, v v = 43π…

Q: The volume of a cube is increasing at the rate of 9 cm3 /  sec. How fast is the surface area…

A:

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…

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.