A cylinder of radius 5 cm and height 10 cm is lowered (circular face first) at a rate of 1 cm/sec into a tall cylinder of radius 15 cm that is partially filled with water. How fast is the water rising at the moment the smaller cylinder is completely submerged?

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. 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: 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 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: Two concentric circles are expanding, the outer radius at the rate of 5 ft/sec and the inner one at…

A: Let A1 and A2 be the areas of the inner and outer circles at any instant and 'A' be the area between…

Q: A ladder 10 ft long leans against a building. If the bottom of the ladder slides away from the…

A: Given A ladder 10 ft long leans against a building. If the bottom of the ladder slides away from 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…

A:

Q: A 25-ft ladder is leaning against a wall. If we push the ladder toward the wall at a rate of 1…

A: Given that

Q: Water is being released from a conical reservoir (vertex down) 20 ft in radius and 40 ft deep at a…

A: Use similar triangle to shoe that  r/20 = h/40 where r and h are the radius and height of water in…

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 cylindrical tank of radius 10 feet is being filled with wheat at the rate of 314 cubic feet per…

A: consider the radius of a cylindrical tank by r. The volume of a cylindrical tank is given as V. The…

Q: A cylindrical tank with radius 5 m is being filled with water at a rate of 2 m3/min. How fast is the…

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Q: Water runs into a sunken concrete hemi- spherical bowl of radius 5 m at the rate of 0.2 m3/sec. How…

A: The derivative gives the rate of change of some variable with respect to other quantity. If a…

Q: A spherical balloon is inflated so that its volume is increasing at the rate of 7 ft^3/min. How fast…

A: given: A spherical balloon is inflated so that its volume is increasing at the rate of 7 ft^3/min.…

Q: A conical water tank has a radius of 3 m and a height of 6 m. Water is flowing into the tank at the…

A: NOTE: Refresh your page if you can't see any equations. . here we have R=3 H=6 V'=12

Q: Water is flowing into a vertical cylindrical tank at the rate of 5 cu ft/min. If the radius of the…

A: Given, water is flowing into a vertical cylindrical tank at the rate of 5 cu ft/min (ie) Volume is…

Q: A cylindrical tank with radius 3 m is being filled with water at a rate of 4 m³/min. How fast is the…

A: Given : The radius of the cylindrical tank is 3 m. Water is filled at a rate of 4 m3/min

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

A:

Q: A 10 ft ladder leans against a wall. If the top of the ladder slides down the wall at a rate of 2…

A:

Q: 2) A 5-ft ladder, leaning against a wall, slips so that its base moves away from the wall at a rate…

A:

Q: A cylindrical tank with radius 8 m is being filled with water at a rate of 3 m3/min. How fast is the…

A: It is known that the volume of the cylinder is V=πr2h where r is radius and h is height. Given that…

Q: A boat is pulled into a dock by a rope attached to it and passing through a pulley on the dock…

A: This problem is based on the application of differentiation.  First we have to write an equation in…

Q: A spherical balloon is increasing in volume at 24t Cm . How fast is the radius ст S. of the balloon…

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Q: A 10-ft ladder is leaning against a wall. If the top of the ladder slides down the wall at a rate of…

A: GivenA 10-ft ladder is leaning against wall .{ HereAB is wallAC is ladder }Let the height of the…

Q: A 25-ft ladder is leaning against a wall. If we push the ladder toward the wall at a rate of 1…

A:

Q: A 50 ft ladder is placed against a wall, as shown below. The base of the ladder is slipping away…

A: Let the horizontal distance of the ladder is = x ft Vertical distance = y ft So, Given that:…

Q: A ladder 20 feet long is leaning against an embankment inclined 60 degrees to the horizontal. if the…

A: The ladder is leaning against an embankment inclined 60 degrees to the horizontal has length 20…

Q: 2. A cylindrical plastic container with a radius of 15 cm is being filled with orange juice at a…

A:

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 spherical balloon is inflated so that its radius increases at a rate of cm/sec. How fast is the…

A: Volume of the sphere is given by:  V = 43πr3

Q: A street light is at the top of a 29 ft pole. A 4 ft tall girl walks along a straight path away from…

A: Draw a diagram that illustrates the given information Let x be the distance to the girl from the…

Q: A 35-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 8…

A: Let BC = x = distance from the base of wall to bottom of the ladderAB = y = distance from the base…

Q: The two equal sides of an isosceles triangle with fixed base b are b are decreasing at the rate of 3…

A: Solution :-

Q: A conical tank has height 3 m3 m and radius 2 m2 m at the base. Water flows in at a rate of 2…

A:

Q: A 17 ft ladder is leaning against a wall. If the bottom of the ladder is pulled along the ground…

A: x2+y2=172=289Differentiate with respect to 't'2xdxdy+2ydydt=0   xdxdt+ydydt=0

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 cylindrical tank with radius 5 m is being filled with water at a rate of 2 m3/min. How fast is the…

A:

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

A:

Q: A liquid is flowing into a vertical cylindrical tabk of radius 6 ft at the rate of 8 ft³/min. How…

A: r=6 ft  &  dVdt=8 ft3min,  where r is the radius, V is the volume at any time t. Let h be the…

Q: An inverted conical tank 10 m high and 3 m radius at the top fills with water at a constant rate. At…

A: Given: An inverted conical tank 10 m high and 3 m radius at the top fills with water at a constant…

Q: A ladder 5 m long rests against a vertical wall. If the top of the ladder slides down the wall at a…

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: A conical glass whose radius is 5m and altitude 12m is being filled at the rate of 10 cu. m/sec. How…

A:

Q: a cylindrical tank with radius 7 m is being filled with water at a rate of 2 m3/ min how fast is the…

A:

Q: A 20-ft ladder is leaning against a wall, and the top of the ladder is sliding down the wall at a…

A: We have been given a 20ft ladder which is leaning against a wall and is sliding down the wall AD.…

Q: A cylindrical tank with radius 5 m is being filled with water at a rate of 3 cu. m / min How fast is…

A: Given, Radius of the cylindrical tank = 5 m Water rate = 3 m3/min

Q: 2. A cylindrical tank standing upright (with one circular base on the ground) has radius 1 meter.…

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Q: A ladder 20 ft long is leaning against an embankment inclined 60° to the horizontal. If the bottom…

A: Let x= distance of ladder from the embankment, y= vertical height. Given: dxdt=-1 ft/sec To find:…

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

A: