Suppose a liquid is to be cleared of sediment by pouring it through a cone-shaped filter. Assume that the height of the cone is 16 in. and the radius at the base of the cone is 4in. If the liquid is flowing out of the cone at a rate of 2in3/min when the level is 8in. deep, how fast is the depth of the liquid decreasing at that instant

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A: Given The volume V of a cube with sides of length x inch Side of the cube is 6inch that is x=6 inch…

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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…

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A: Differentiate volume wrt t

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

A: Given: The trough is being filled with water at the rate of 0.3 m3/min, dVdt=0.3 m3/min

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Q: A spherical iron ball 8 in. in diameter is coated with a layer of ice of uniform thickness. If the…

A: A spherical iron ball 8 in. in diameterSo radius = 8/2 = 4 inchLet the ice on the ball is x inches…

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Q: A spherical iron ball 10 in. in diameter is coated with a layer of ice of uniform thickness. If the…

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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) 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…

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A: The volume of hemisphere filled with liquid to height h = πrh2-π3h3

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A: Solve by diagram and using formulas of equilateral triangle

Q: The volume V of a cube with sides of length x in. is changing with respect to time. At a certain…

A: Solved below

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A:

Q: Let l be the length of a diagonal of a rectangle whose sides have lengths x and y, and assume that x…

A: Now in triangle ABC, by using Pythagorean theorem, we get

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A: Given: Length of cube L=3cm Rate of melting =-2cm3

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A: We have to find the rate at which the level of the solution in the cylinder rising.

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: 2. Suppose that the bottom of a conical shaped tank of water has been ruptured. At the instant when…

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Q: Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a…

A: Given that radius =7 ft dVdt=9 cubic ft per minutefind dhdt Also V=πr2h

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Q: A funnel in the shape of an inverted cone is 30 cm deep and has a diameter across the top of 20 cm.…

A: Geometry

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A: Let,  r - radius of the right circular cone h-Height of the right circular cone  V- Volume of the…

Q: The original 24 m edge length x of a cube decreases at the rate of 2 m/min. a. When x = 4 m, at what…

A: As Given :                   The length x of Cube decrease at a rate of 2 m/min.…

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A: Solution: Consider the given that conical reservoir 24ft (h) deep and 12ft across the top that is…

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Q: The radius of a sphere, initially zero, increases at the rate of 6 ft per second. How fast the…

A: Given ,The radius of a sphere , initially zero , increases at the rate of 6 per second.The volume is…

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Q: Suppose that a cube's volume increases at a constant rate of 2 m. How fast are it's sides growing at…

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Q: coffee is draining out of a conical filter at a rate of 2.25 inches cubed per minute. If the cone is…

A: given: coffee is draining out of a conical filter at a rate of 2.25 inches cubed per minute. If the…

Q: A spherical iron ball 8 in. in diameter is coated with a layer of ice of uniform thickness. If the…

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Q: A horizontal trough is 16m long, and its ends are isosceles trapezoids with an altitude of 4m, a…

A: The derivative is also called the rate of change of a quantity with respect to time. The volume of a…

Q: The volume of a cube is increasing at the rate of 9 cm3 /  sec. How fast is the surface area…

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Q: Let l be the length of a diagonal of a rectangle whose sides have lengths x and y, and assume that x…

A: Given that,  'L' be the length of a diagonal of a rectangle whose sides have lengths x and y, and x…

Q: A spherical iron ball 12 in. in diameter is coated with a layer of ice of uniform thickness. If the…

A: Given problem:- A spherical iron ball 12 in. in diameter is coated with a layer of ice of uniform…

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…