The radius of a sphere is increasing at a rate of 5 mm/s. (a) How fast is the volume increasing when the diameter is 60 mm? (b) How fast is the surface area increasing when the diameter is 60 mm?

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Q: 3. The radius of a spherical balloon is increasing at the rate of 2 cm per minute. How fast is the…

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Q: A spherical balloon is inflated at a rate such that it's radius increases at a rate of 500…

A: rate of change in volume = 307876.08 detailed solution with explanation is given below

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

A: Given Data: The radius of the cylindrical tank is: r=5 m The rate of increase in volume is: V'=3…

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

A: Given:                                 Volume of a right circular cylinder V…

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 circle is inside a square. The radius of the circle is increasing at a rate of 1 meter per day and…

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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: Oil from an uncapped well is radiating outward in the form of a circular film on the surface of the…

A: Let r and A be the radius and area of the circle respectively at time t. The radius of the circle is…

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

A: V=43πr3

Q: A 6-ft-diameter cylindrical tank is filled with water to a height of 10 ft. It is drained such that…

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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: 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 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: 4. A cylindrical tank with radius 5 m is being filled with water at a rate of 3 m3/min. How fast is…

A: We know  (V) volume of cylinder =πr2h. r= radius of cylinder h= height of cylinder  V= volume of…

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

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Q: A board 15 feet long slides down a wall. At the instant the bottom end is 12 feet from the wall, the…

A: A board 15 feet long slides down a wall. At the instant the bottom end is 12 feet from the wall, the…

Q: cylindrical tank with radius 5m is being filled with water at a rate of 3m3/min. How fast is the…

A:

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: An isosceles triangular water trough is 5 meters long, 3 meters across the top, and 2 meters deep is…

A: Where we see the application of derivatives to solve the given problem

Q: A circle is inside a square. The radius of the circle is decreasing at a rate of 4 meters per minute…

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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: 5. The sides of a square are increasing at a rate of 10 cm/sec. How fast is the area enclosed by the…

A: Solution

Q: A spherical balloon is inflated so that its volume is increasing at the rate of 2 ft3/minft3/min.…

A: Given: A spherical balloon is inflated so that its volume is increasing at the rate of 2 ft3/min.…

Q: An artist paints a portrait on a circular canvas and encloses it in a circular metal frame. At a…

A: Let the radius of the circular canvas be r.   The area of the canvas will be given by: A=πr2   Also,…

Q: How do you solve question 1?

A: The relation between volume of a sphere and the its radius is given as, Where  V: Volume r: Radius

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

A: Given: A stone dropped into a still pond sends out a circular ripple whose radius increases at a…

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

A:

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

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

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Q: A spherical balloon is to be inflated so that its volume increases at a rate of 800m cm'/min. How…

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Q: A spherical balloon is being inflated. The volume is increasing at a rate of 5 mm per second. How…

A: Given: The volume of a spherical balloon is increasing at the rate of 5 mm3/sec. The diameter of…

Q: An isosceles triangular water trough is 6 meters long. 3 meters across the top, and 2 meters deep is…

A:

Q: A circle is inside a square. The radius of the circle is decreasing at a rate of 5 meters per…

A: Let r be the radius of circle ands be the length of the side of squareGiven: drdt=-5 and ds/dt=5Let…

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: 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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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…