Suppose the radius of a sphere are expanding at a rate of 6 inches per minute. How fast is the volume of the sphere changing at the moment the diameter is 12 inches?

Q: Suppose that the sides of a cube are expanding at a rate of 2 inches per minute. How fast i the…

A: We need to find the rate of change of volume of cube when side is 20 inches. Volume of cube=(side)3…

Q: The sides of a square are increasing at the rate of 2 inches per minute. How fast is the Area…

A: Given The side of square is increasing at rate of 2inches per minute.  The area of a square with…

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: All edges of a cube are expanding at a rate of 3 centimeters per second. (a) How fast is the surface…

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

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Q: Each side of a square is 6 ft and is increasing at a rate of 2 ft per second. How fast is the area…

A: By differentiating equation of area of square with respect to time and substituting the value of…

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: Suppose that the sides of a cube are expanding at a rate of 2 inches per minute. How fast is the…

A: all details are given in below. please check it

Q: A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 3…

A: Given that:Rate of increase of radius, drdt=3 ft/s

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…

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: Suppose the sides of a cube are expanding at a rate of 2 inches per minute, How fast is the volume…

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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: Water is pouring from a hole at the rate of 25 cu. m per minute and is forming a conical pile on the…

A: This question can be solved by applying the concept of rate of change of physical quantities.

Q: A spherical balloon is being deflated at a rate of 80 cm3/min. At what rate is the radius decreasing…

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

A: Let r be the radius of spherical ballon

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: 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: How fast is the circumference of a circle changing if the radius is changing at the rate of 3 mm/s?

A: Solution

Q: If the sides of an equilateral triangle are increasing at a rate of 6 m/min. How fast is the area of…

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Q: All edges of a cube are expanding at a rate of 2 centimeters per second. (a) How fast is the surface…

A: All edges of a cube are expanding at a rate of 2 centimeters per second.

Q: A conical reservoir is losing water at the rate of 12 cubic feet per minute. If the radius is % the…

A: Let the height of the conical reservoir be h. Then the radius will be = h/4 Therefore we get the…

Q: The volume of a cube is increasing at a rate of 9 cubic centimeters per second .How fast is the…

A: Solution:-

Q: All the edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the volume…

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Q: A Ferris wheel with a radius of 13m is rotating at a rate of one revolution every 2 minutes. How…

A: Given thatRadius of the Ferris wheel is 13 mThe time period of the Ferries wheel is 2 min To find…

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: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the surface…

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Q: at a certain instant, the dimensions of a rectangle are 8 and 12 feet and they are inreasing at the…

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Q: If the radius of a right circular cylinder is increasing at a rate of 1 inch per minute, and the…

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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: Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the…

A: Given oil is spilled from tank and it flowing  in a circular path with increasing radius of 2m/s .…

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. How fast is the surface…

A: Since, we have been given that all edges of a cube are expandingat a rate of 8 centimeters per…

Q: Suppose the radius of a sphere is expanding at a rate of 3 inches per minute. How fast is the volume…

A: Let V & r be the volume and radius of the sphere at any time t respectively. Given that, the…

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: The radius of a sphere is increasing at a rate of 4 meters per minute. When the radius is 11 meters,…

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Q: as a balloon in the shape of a sphere is being blown up, the volume is increasing at the rate of 4…

A: Volume of the sphere Shape ballon: V = 4/3ℼr3   (r = radius)   Now differentiate with respect to L,…

Q: A spherical balloon is being deflated at the rate of 10 cm/s. What is the rate of change for the…

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Q: how

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Q: A cone shaped icicle has an initial radius of 10 inches and a height of 15 inches. Once the height…

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Q: When a metal plate is heated, it expands. If the shape of the plate is circular and its radius is…

A: When a metal plate is heated, it expands. If the shape of the plate is circular and its radius is…

Q: The radius of a sphere, initially zero, increases at the rate of 4 feet per second. Find how fast…

A: Solution :Given  the adius of a sphere, initially zero, increases at the rate of 4 feet per…

Q: How fast is the surface area of a cu

A: Given that : Edge of a cube = 30 cm Th edge changing at the rate of 3 mm per second.

Q: All edges of a cube are expanding at a rate of 6 centimeters per second. (a) How fast is the surface…

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Q: The side of a square sheet is increasing at rate of 4 cm per minute ,At what rate is the area…

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Q: A rectangle has a length that is increasing at a rate of 16 mm per second with the width being held…

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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…