A conical paper cup is 30 cm tall with a radius of 10 cm. The bottom of the cup is punctured so that the water level goes down at a rate of 3 cm/sec. At what rate is the volume of water in the cup changing when the water level is 4 cm?

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A: we know third law of equation of motionv2=u2+2aswhen ball reaches to highest point then final…

Q: find the rate at which the volume of a right circular cylinder of constant altitude 10 feet changes…

A: Given  Altitude=10feet We need to find the rate at which the volume of a right circular cylinder…

Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of  6cm/min.…

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Q: The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is…

A: Given that, drdt=1.1 in/s and dhdt=-2.7 in/s. Also, it is given that r=102 in. and h=162 in. It is…

Q: A 5 ft long ladder rests against a vertical wall. If the bottom of the ladder slides away from the…

A: Let's understand what's going on:

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

A: we have given that Gas is being pumped into a spherical balloon at the rate of 10 cubicinches per…

Q: A rectangular trough is 10ft. long and 3ft. wide. Find how fast the surface rises, if water flows in…

A: Since you have asked multiple questions in a single request we will be answering only the first…

Q: A water tank has the shape of an inverted circular cone (point down) with a base of radius 6 feet…

A: We can consider two similar triangles from the question and using that we can make an expression for…

Q: Water is poured into a conical paper cup at the rate of 3/2 in/sec (similar to Example 4 in Section…

A: I will use the formula V=13πr2h and differentiation method to solve this problem.

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

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Q: Sugar is poured into a conical tank at the rate of 15cm3/sec whose bottom radius is always quarter…

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Q: if the base of triangle is constantly 4 cm find the rate at which the area of the triangle is…

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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: Air is being pumped into a spherical balloon at a rate of 5 cubic centimeters per minute. Determine…

A: Given : The air is pumped into a balloon at a rate of 5 cm3/min The diameter of the balloon is 20 cm

Q: A trough of water is 8 meters in length and its ends are in the shape of isosceles triangles whose…

A: Given:- A trough of water is 8 meters in length and its ends are in the shape of isosceles triangles…

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: Water is flowing at the rate of 9 ft3/min into a tank that is in the shape of a right circular…

A: Let r be the radius of base of cylinder, then r=2 ft .Let h be the height of water level at any time…

Q: 2. please help, they canceled class due to virus can't contact teacher.

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

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Q: A spherical snow ball is being made so that its volume is increasing at the rate of 8 ft /min. What…

A: given: dVdt=8 ft3 /min We have to find drdtwhen diameter of snowball is 4 ft i.e, radius= 2ft we…

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

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Q: As a circular metal griddle is being heated, its diameter changes at a rate of 0.01 cm/min. Find the…

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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: 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 at the rate of 6 ft/min into a tank that is in the shape of a right circular…

A: Given data:   The rate at which water is flowing in the cylindrical tank is dV/dt =6 ft3/min. The…

Q: A softball diamond is a square whose sides are 60 ft long. Suppose that a player running from first…

A: Suppose , y is the distance from the home and x is the distance from first base. Given that ,…

Q: a water tank has the shape of an inverted circular cone with a base radius of 2m and a height of 4m.…

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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: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15 cm/min.…

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Q: If the radius of a sphere is increasing at a constant rate of 3 cm/sec, then the volume is…

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Q: Imagine a sphere whose radius r increases at a rate of 3 cm/s. At what rate is the volume V of the…

A: Note the results : Volume of the sphere is 43πr3 . Suppose F is a function of x and x is a function…

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: A spherical snowball is made so that its volume is increasing at a rate of 8 cubic feet oer minute.…

A: I set these up this way. what do we know?  dVdt= 8 ft 3/min What do we want?  drdt = ?   when d = 4…

Q: A ball is shot straight up into the air with initial velocity of 47 ft/sec. Assuming that the air…

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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: A ball is shot from the ground straight up into the air with initial velocity of 42 ft/sec. Assuming…

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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: 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: 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 comet loses material when it gets close to the Sun at a rate of 100 cubic meters per minute.…

A: Given Comet is a sphere Its radius is 200 meters Let V be the volume of the comet then r be the…

Q: The sides of a square increases in length at a rate of 3 m/sec. At what rate is the area of the…

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Q: A right circular cylinder has a radius increasing at the rate of 4 cm per second but its total…

A: A right circular cylinder has a radius increasing at the rate of 4 cm per second but its total…

Q: A gas line-driven lawnmower has a blade that extends out 1 foot from its center. The tip of the…

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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: A 20-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 6…

A: Let x= horizontal distance y=vertical distance Given that dx/dt=6 ft/sec and x=16 ft At x=16 we find…

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

A: