A cone with an altitude of 50 cm has its base radius changing at the rate of one millimeter per second. How fast is its volume changing when the radius is 20 cm?

Q: Suppose the radius of a sphere are expanding at a rate of 6 inches per minute. How fast is the…

A: Let us suppose the radius of sphere be R. Given that :   dRdt=6 incheminute.  Radius=Diameter2=122=6…

Q: The edges of a cube are expanding at a rate of 5cm per second. How fast is the volume changing when…

A:

Q: All edges of a cube are expanding at a rate of 9 centimeters per second. (a) How fast is the volume…

A: GivenAll edges of a cube are expanding at a rate of 9 centimeters per second

Q: A conical vessel 12 cm deep and with a radius of 6 cm at the top, is being filled with water. If the…

A: A conical vessel 12 cm deep and with a radius of 6 cm at the top. That is, the height of the cone is…

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 spherical balloon is increasing at the rate of 0.8 cm / minute. How fast is 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: 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: the

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Q: The volume of  a cube is increasing at a rate of 9 feet3/sec . how fast is the surface area…

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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 ladder 20 ft. long leans against a vertical wall. If the top slides downward at the rate of 2…

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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: 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: 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: 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: When a circular plate of metal is heated in a oven, its radius increases at a rate of 0.05 cm/min.…

A: drdt=0.05cm/minradius, r=52cmArea=πr2Derivative formuladdxxn=n xn-1

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: The radius of a right circular cone is increasing at a rate of 5 inches per second and its height is…

A:

Q: The volume of a cube is increasing at the rate of 8 cm /sec.How fast is the surface area in creasing…

A: We can find the answer as below

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

A:

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: All edges of a cube are expanding at a rate of 7 cm per second. How fast is the surface area…

A: Given that all edges of a cube are expanding at a rate of 7 cm per second. Let the edge of a sphere…

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 trough filled with water is 2m long and has a cross section in the shape of an isosceles trapezoid…

A:

Q: A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 2…

A: Given ,  A stone dropped in a pond sends out a circular ripple whose radius increases at a constant…

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 snowball is melting at a rate of 1 cm3 per second. If it remains spherical, how fast is the…

A:

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: All edges of a cube are expanding at a rate of 9 centimeters per second. How fast is the volume…

A:

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

A:

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 water trough is 10 m long and a cross-section has the shape of an isosceles trapezoid that is 30…

A:

Q: A cylindrical tank with radius 6 m is being filled with water at a rate of 4 m3/min. How fast is the…

A: From the given information it is given that:Radius of cylindrical tank(r) = 6mRate at which the…

Q: A conical cup is 4 cm across and 6 cm deep. Water leaks out of the bottom at the rate of 2 cm3 /sec.…

A:

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: 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…

Q: A 3-meter long steel pipe has its upper end leaning against a vertical wall and lower end on a level…

A: Given that, Length of pipe is 8m, lower end moving away at the rate of 2 cm/sec. we have to find how…