3. Gas is escaping from a spherical balloon at the rate of 2 cm³/min. Find the rate at which the surface area is decreasing, in cm?/min, when the radius is 8 cm.

Q: Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the…

A:

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A: Diameter= DRadius = r =D/2Surface area = A= 4pi*r^2Given dA/dt= -1 cm^2/min (negative because…

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A: Differentiate volume wrt t

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Q: 2. A balloon in the shape of a sphere is being inflated at the rate of 100 cm/sec. a. At what rate…

A: a)  Given that the balloon is in the shape of sphere and it is being inflated at the rate of…

Q: 1. A boy is blowing a spherical balloon at a rate of 50 cm /s. At what rate is the radius of the…

A: This question is based on application of derivative.

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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: Suppose the radius of a sphere is increasing at a rate of 5 in/second.  At what rate is the surface…

A: Given that radius of a sphere is increasing at an of 5 in/sec. Let r be the initial radius of the…

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Q: A cube’s surface area increases at the rate of 72 in2/sec. At what rate is the cube’s volume…

A: Given:

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A: The rate of evaporation is proportional to the exposed surface, and the exposed surface is that of a…

Q: 8. The radius of an inflating balloon in the shape of a sphere is changing at a rate of 3cm/sec. At…

A:

Q: The original 24 m edge length x of a cube decreases at the rate of 3 m/min. a. When x = 4 m, at what…

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Q: If a snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate at…

A:

Q: 9) A spherical snowball is melting in such a way that its volume is decreasing at a rate of 3cm /…

A: Let, r=radius  V=volume Given that dV/dt= 3 , we have to find dr/dt=? at r=12 cm Volume and radius…

Q: A cone-shaped tank of water is leaking water at a constant rate of 3 m³/hour. If the base radius of…

A: Using volume  of cone and applications of derivative idea we solve this

Q: If a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate at…

A:

Q: The radius of a right circular cone is increasing at a rate of 1.2 in/s while its height is…

A: To calculate the required rate of change using partial derivatives

Q: 16. If the radius of a circle is increasing at the rate of 4 cm/s, find the rate of the increase in…

A: Given radius of a circle is increasing at the rate of 4 cm/sec.

Q: 12) A vertical cylinder is leaking wader at a rate I ft3% If the cylinder har a height of 10t Sec.…

A: Volume of cylinder = πr2h  r= radius of cylinder  h= height of cylinder

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

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Q: The original 24 m edge length x of a cube decreases at the rate of 2 m/min. a. When x = 1 m, at what…

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Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15 cm/min.…

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Q: at what rate is the volume of the cube changing if the edge is 8cm and is changing at 4cm/sec?

A: The volume of a cube is: Where, a is the edge of the cube. Formula used:

Q: If a snowball melts so that its surface area decreases at a rate of 4 cm2/min, find the rate at…

A: To find the rate at which the diameter decreases when the diameter is 12 cm and surface area…

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A:

Q: Suppose that a tumor in a person’s body has a spherical shape and that treatment is causing the…

A: we know that the volume of the sphere                       V=43πr3                          (1)

Q: As an orange grows, the rate of change of the radius r of the orange is inversely proportional to…

A: Given query is to find differential equation.

Q: Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the…

A:

Q: A cone-shaped tank of water is leaking water at a constant rate of 2 m3/hour. If the base radius of…

A: Given that

Q: A spherical snowball is melting in such a way that its surface area decreases at the rate of 1…

A:

Q: The radius of a right circular cone is increasing at a rate of 5 in/s while its height is decreasing…

A: Let,  r - radius of the right circular cone h-Height of the right circular cone  V- Volume of the…

Q: 11. At what rate is the volume of the cube changing if the edge is 8 cm and is changing at 4 cm/s?

A: As we know that; The expression for the volume of the cube with the edge length ''a'' is: v=a3…

Q: A cube is expanding in such a way that the length of its diagonal is increasing at a rate of 5…

A: Let y be the diagonal, x be the length of an edge and V be the volume of the cube at any time t.…

Q: 1. A spherical balloon is expanding. If the radius is increasing at the rate of 2 inches per minute,…

A: The given question can be solved as shown in step2.

Q: Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the…

A:

Q: 4. A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15…

A:

Q: If a spherical balloon is being filled with air at a constant rate of 2 cm³/s, at what rate is the…

A: Let r be the radius of the balloon in cm and V be the volume in cm3. The variable t stands for time…

Q: 15. Water is being poured at the rate of 150 cm³/s into an inverted cone with a diameter of 3 meters…

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Q: If the radius of a sphere increases at a rate of 0.5 m/sec, then the rate at which the volume of the…

A: Let the radius of the sphere be r. Then the volume of the sphere is: V=43πr3…

Q: An inverted conical tank 10 m high and 3 m radius at the top fills with water at a constant rate. At…

A: Given: An inverted conical tank 10 m high and 3 m radius at the top fills with water at a constant…

Q: Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the…

A: