A water tank is in the shape of a right circular cylinder with height of 4 meters and radius of 2 meters. Water is being poured onto this tank at a rate of 4 cubic meters per minute. How fast is the water level rising if the water level is 1 meter high?

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: 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: A water tank is in the form of an inverted right circular cone h feet deep and d feet wide across…

A: Consider the following:

Q: A submarine started at the surface of the ocean and began diving -15 kilometers per minute towards…

A: Given: Diving speed of submarine, s = 15 km/min, and time of diving, t = 48 min

Q: A Ferris wheel with a radius of 10 m is rotating at a rate of one revolution every 2 minutes. How…

A: the height is given byh = 10 sin (pi * t) + 10dh/dt = 10 cos (pi * t) * pi

Q: A plane is flying at a constant altitude of 1 mile and a speed of 400 mph toward an observer on the…

A: The plane is flying at a constant altitude of 1 mile. Let x be the horizontal distance and y be the…

Q: The sides of an equilateral triangle are increasing at a rate of 12 inches per minute. At what rate…

A: Area of equilateral triangle A=/--3/4 a2 Here a = side of the equilateral triangle Differentiate A…

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 cylindrical pool has a height of 8 feet and a radius of 6 feet. How fast is the volume of the…

A: Here we solve the given problem of calculus.

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: A rectangular tank with a square bottom has base side lengths of 3 feet and a height of 10 feet is…

A: Given that the base of the tank is a square and shape of the tank is rectangular. Also base side…

Q: The volume of a cube is increasing at the rate of 21 cc/min. At what rate is its surface area…

A: The volume of a cube is increasing at rate, dVdt = 21 cc/min To evaluate: The rate at which the…

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Q: A baseball diamond has the shape of a square with sides 90 feet long, suppose the player is running…

A: It is given that a baseball diamond has the shape of square with side 90 feet long. Construct the…

Q: A trough is 10 feet long and its ends have the shape of isosceles triangles that are 3 feeta cross…

A: To find: The rate of incresing level of the water. Given information: The trough is 10 feet long…

Q: A 6-ft-diameter cylindrical tank is filled with water to a height of 10 ft. It is drained such that…

A:

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: The sides of an equilateral triangle are increasing at a rate of 10 cm/min. At what rate is the area…

A: let side of triangle = x    Given

Q: a) Water is flowing into a leaky cistern at the rate of 31.4 cu ft./min. The cistern is a right…

A: Given that  The water is flowing into a leaky cistern at the rate of 31.4 cu ft./min ⇒dVdt=31.4…

Q: How fast is the area of the circle of the ripples expanding at the instant that the radius of the…

A:

Q: Given the question: A tank shaped like a right circular inverted cone with radius 5 meters and…

A:

Q: A water trough is 8 feet long, and its cross section is an equilateral triangle with sides 4 feet…

A: (a) Height of an equilateral triangle of side length s, is given by, h=3s2 ft

Q: A baseball diamond has the shape of a square with side 90 feet long. A player running from second…

A:

Q: A conical water tank with vertex down has a radius of 10 ft at the top and is 24 ft high. If water…

A:

Q: The original 24 m edge length of a cube decreases at the rate of 2 m divided by two minutes When x=1…

A:

Q: A plane is flying at a constant altitude of 1 mile and a speed of 400 mph toward an observer on the…

A:

Q: A plate in the shape of an equilateral triangle expands with time. The length of a side increases at…

A: Given that the length of side increases at a constant rate of 2 cm/h find out at what rate is the…

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: Water flows out of a hemispherical tank at a rate which is 4 times the square root of its depth. If…

A: GIVEN: Radius of the tank is 8 ft

Q: A girl is using a straw to drink coke from a right cylindrical glass at a rate of 6 cubic…

A:

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

A:

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 cylindrical pool has a height of 8 feet and radius of 6 feet. How fast is the volume (in cubic…

A: Volume of cylindrical shape V=πr2h ------------------(1)

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: A water tank is in the form of a right circular cone with vertex down, 12 ft. deep and 6 feet across…

A: Given: height, h=12 ft., radius, r=62=3 ft., and dVdt=10 ft3/minTo find, The rate at which the water…

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

A: The volume of water trough = Area × Length Area of trapezium = 12×Sum of parallel sides×height…

Q: A tank is shaped like an upside-down square pyramid, with a base with sides that are 4 meters in…

A:

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: A baseball diamond has the shape of a square with sides 90 feet long. A player running from first…

A: The rate is:-

Q: The volume of a cube is increasing at the rate of 2 cubic inches per minute. How fast is the surface…

A:

Q: The base of a 20-foot ladder is sliding toward a wall at a rate of 1.5 feet per second. How fast is…

A: We solve the above problem.