Water in an open bowl evaporates at a rate proportional to the area of the surface of the water. (This means that the rate of decrease of the volume is proportional to the area of the surface.) Show that the depth of the water decreases at a constant rate, regardless of the shape of the bowl.

Q: The volume of a cube decreases at the rate of 84 m /sec. The rate at which the side of т the cube…

A: To find the rate at which the side length of cube changed when side is equal to 8 m/s

Q: hot air ballon is hovering 110 meters above the ground and begins to assend at a rate of 17 meters…

A: This is a question of application of differentiation and integration... We will proceed as follows

Q: a snowball melts in such a way that the rate of change in its volume is proportional to its surface…

A: Please see the below pictures for detailed solution.

Q: A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius…

A: Rate of Radius of outer ripple increasing = 1 ft/sec                    Radius = 4 feet

Q: The volume of a sphere is.5 increasing at the rate of 3 cubic centimeters per second. Find the rate…

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Q: Is the rate of change of a cube's volume linearly proportional to the rate of change of its side?

A: Rate of change of volume of cube

Q: The side of a cube decreases at a rate of 7 m/sec. Find the rate at which the volume changes, when…

A: Side of a cube decrease at rate of 7m/s Rate of change in volume?

Q: An inverted pyramid is being filled with water at a constant rate of 55 cubic centimeters per…

A: Introductions :We have given an inverted pyramid.water rate = 55 cm3/secside length = 7 cm height =…

Q: The volume of a sphere is increasing at a rate of 8 cubic cm/sec.  Find the rate of change of its…

A: Let V be the volume of the sphere which is given in the question as,

Q: A faucet is filling a hemispherical basin of diameter 60 cmwith water at a rate of 2L/min . Find the…

A:

Q: The height of a rectangular box is 10 in. Its length increases at the rate of 2 in./sec; its width…

A: Volume of rectangular box = l b hwhere, l = length of boxb= width of boxh = height of boxRate of…

Q: Air is being pumped into a spherical balloon at a rate of 5 cubic cm per minute (cm3/min) ,…

A: Air is being pumped into a spherical balloon at a rate of 5 cubic cm per minute (cm3/min)

Q: A spherical snowball melts at a rate proportional to its surface area. Show that the rate of change…

A: Given that spherical snow ball melts at a rate proportional to its surface areaShow that rate of…

Q: An inverted pyramid is being filled with water at a constant rate of 65 cubic centimeters per…

A:

Q: Example: Find the rate of change of the volume of a cylinder with respect to r if h = 10m.

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Q: The base of a triangle is shrinking at a rate of 6cm/s and the height of the triangle is increasing…

A: The rate of change of the area with respect to time is the derivative of the area function with…

Q: An inverted pyramid is being filled with water at a constant rate of 75 cubic centimeters per…

A: The rate at which water level is rising when the level is 5cm is 25cm/sec.

Q: An inverted pyramid is being filled with water at a constant rate of 55 cubic centimeters per…

A:

Q: An inverted pyramid is being filled with water at a constant rate of 45 cubic centimeters per…

A:

Q: An inverted pyramid is being filled with water at a constant rate of 25 cubic centimeters per…

A: The volume of the pyramid is                        V=13Bh Where B is the area of the base…

Q: The radius of a sphere decreases at the rate of 4 m/s. when the radius is 10m, then the rate of…

A: We will find the rate of change in surface area as following .

Q: One airplane is approaching an airport from the north at 128 km/hr. A second airplane approaches…

A: Let x be the distance of south bound plane and y be the distance of west bound plane from airport at…

Q: An inverted pyramid is being filled with water at a constant rate of 70 cubic centimeters per…

A:

Q: Find the surface area of a sphere at the instant when the rate of increase of the volume of the…

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Q: The linear density of a cable wire is the rate of change of its mass with respect to its length. A…

A:

Q: An inverted pyramid is being filled with water at a constant rate of 45 cubic centimeters per…

A:

Q: The volume V of a right circular cone of radius r and height h is given by V = 1/3 πr2h. a) What is…

A: Simply take derivative with respect to given variable considering other as constant.

Q: 15. Gas is being pumped into a spherical balloon at the rate of 10 cubic inches per second. When the…

A: NOTE: Refresh your page if you can't see any equations. . here we have the diameter is 30 inches so…

Q: Suppose you are drinking root beer from a conical paper cup. The cup has a diameter of 8 cm and a…

A: Given, The diameter of a conical paper cup is 8 cm Therefore, the radius of the cup is 4 cm The…

Q: A balloon has just been inflated. Calculate the instantaneous rate of change by which the area…

A: Introduction: A geometric shape with a sphere-like appearance. In three dimensions, the sphere is…

Q: The edge of a cube decreases at a rate of 1.5m/s. Find the rate at which the surface area decreases…

A:

Q: An inverted pyramid is being filled with water at a constant rate of 35 cubic centimeters per…

A: Finding the rate at which water level rises in a pyramid at a particular height

Q: Find the rate of change of the surface area of the cube when the volume is 8 cm". A block of ice in…

A:

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

A: Given query is to find the rate at which diameter of snowball is decreasing.

Q: A tank contains 100 L of water. A salt solution containing 2 kg of salt per liter flow in at the…

A:

Q: An inverted pyramid is being filled with water at a constant rate of 35 cubic centimeters per…

A:

Q: A snowball melts in such a way that the rate of change in its volume is proportional to its surface…

A:

Q: The sides of a cube increase at a rate of K cm/s. When the sides have a length of 2 cm, the rate of…

A:

Q: An inverted pyramid is being filled with water at a constant rate of 25 cubic centimeters per…

A: Given inverted square pyramid has length of square base b=2 cm and height h=5 cm Water is being…

Q: An inverted pyramid is being filled with water at a constant rate of 75 cubic centimeters per…

A:

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: A right circular cylinder has a 4 inch diameter and is filling with water at a constant rate.  The…

A: Consider the volume of right circular cylinder V. Differentiate it w.r.t time t.…

Q: An inverted pyramid is being filled with water at a constant rate of 40 cubic centimeters per…

A:

Q: An inverted pyramid is being filled with water at a constant rate of 55 cubic centimeters per…

A:

Q: A cement mixer is pouring concrete in a conical pile. At the time when the height and base radius of…

A:

Q: An inverted pyramid is being filled with water at a constant rate of 45 cubic centimeters per…

A: We know, Volume of a figure = Area of a base × Height

Q: The radius of a sphere decreases at the rate of 5 m/s. when the radius is 10m, then the rate of…

A:

Q: The radius of a sphere is decreasing at a rate of 2 centimeters per second. At the instant when the…

A: Write the equation of the surface area of sphere solve it as per given in step 2