15. Gas is being pumped into a spherical balloon at the rate of 10 cubic inches per second. When the diameter is 30 inches, find the rate at which the radius is changing and the rate at which the surface area is changing?

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

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Q: O. At what rate is the vertex angle of a right circular cone changing when the radius is 3 ft and…

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Q: 23. Suppose that water is stored in a cylindrical tank of radius 5 m. If the height of the water in…

A: Consider the given information

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A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

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Q: 11. If the base of a triangle is constantly 4 cm, find the rate at which the area of the triangle is…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

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.

Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 10 cm/min.…

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Q: 2)The radius of a sphere decreases at the rate of 1 m/sec. Find the rate at which the volume…

A: Given,  The radius of a sphere decreases at the rate of 1 m/sec  We have to find the rate at which…

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

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Q: You are blowing air into a spherical balloon at a rate of cubic inches per second. (The reason for…

A: You are given V'(t), which is    V'(t) = 4pi/3   From there you know   V(t) = (4pi/3) * t   You also…

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: 3. Water is flowing into a vertical cylindrical tank at the rate of 24 cubic ft. /min. if the radius…

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Q: 2. The radius of a sphere decreases at the rate of 5 m/sec. Find the rate at which the volume…

A: Given that the Radius of sphere decreases at the rate of 5m/sec and radius is 5 m

Q: The sides of a square increase in length at a rate of 4 m/sec. a. At what rate is the area of the…

A: Area of square = a2 Where a is length of side of square.

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: 1. We are inflating a spherical balloon. At what rate is the volume of the balloon changing when the…

A: Since you have asked multiple question (1&2) we will solve the first question for you. . If you…

Q: 2)The radius of a sphere decreases at the rate of 4 m/sec. Find the rate at which the volume…

A: We need to find the rate at which volume decrease when radius is 3m

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

Q: Suppose that a drop of mist is a perfect sphere and that, through condensation, the drop picks up…

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Q: 3) If a spherical snowball melts so that its surface area decreases at a rate of 1 cm? he rate at…

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Q: 1.) Water is pouring into a conical vessel 15 cm deep and having a radius of 3.75 cm across the top.…

A: step by step clear explanation is given .Have a look

Q: 13. A water tank at a filtration plant is built in the shape of an inverted cone with height 5.2 m…

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Q: 15) The volume of a sphere is increasing at a rate of 6 cm³/sec. Find the rate of change of its 4T…

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Q: 17. If the radius of a sphere is increasing at the constant rate of 3 inches per second, how fast is…

A: Given: The radius of the sphere is increasing at the constant rate of 3 inches per second. To find:…

Q: 6. The radius of a right circular cylinder is increasing at the rate of 3in/sec, while the height is…

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Q: 7. A spherical balloon is being filled in such a way that the surface area is increasing at a rate…

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

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Q: 1. The side of a cube increases at the rate of 12 m/sec. Find the rate at which the volume of the…

A: Our guidelines for multiple questions,answer only first question For other answers , Repost this…

Q: 2. The radius of a sphere is decreasing slowly at the rate of 2 cm/week. How fast is the volume…

A: Consider the given information. The volume of the sphere is defined as, V=43πr3

Q: 1. The radius of a sphere increases at a rate of 2 m/sec. The rate at which the volume increases…

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Q: 2)The radius of a sphere decreases at the rate of 1 m/sec. Find the rate at which the volume…

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Q: 2. The volume of a cube decreases at a rate of 10m/sec. Find the rate at which the side of the cube…

A: dVdt=10m3/min, side=2mFormula of volumeV= side3

Q: 4. Water is running out of a conical tank 3 m across the top and 4 m deep at the rate of 2 m3 /min.…

A: given  h = 4 m  (Note: measurement of h is always taken from bottom) r = (3 ÷ 2 ) = 1.5 m dVdt = 2…

Q: 4 mm/s when these three sides are 5cm, 4 cm sides x, y and z increase at 6 mm/s, 5 mm/s and Fig.…

A: we have to find rate of change of AC.

Q: 14. As sand leaks out of a hole in a container, it forms a conical pile whose altitude is always the…

A: We have to find the rate at which the sand is leaking out when the height is 10 in.  Or we can say…

Q: 2) The radius of a sphere decreases at the rate of 4 m/sec. Find the rate at which the volume…

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Q: 2)The radius of a sphere decreases at the rate of 1 m/secm/sec. Find the rate at which the volume…

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Q: 2. The height and volume of a right circular cone change at the rates of 1 cm/s and -2 cm^3/s,…

A: Let's find.

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

A: Volume of sphere: V = 43πr3, where r is radius of sphere. Surface area of sphere: S = 4πr2, where r…

Q: 3. A water tank has the shape of an inverted circular cone with base radius 4 m and height 8 m. If…

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

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