2. Suppose that the bottom of a conical shaped tank of water has been ruptured. At the instant when the depth of water is 4 ft, it is decreasing at a rate of 2 ft per minute. How fast is the volume of water in the tank being depleted at that instant if the radius of the tank is twice its height?

Q: 2. Sand is being dropped at the rate of 10ft.3/min into a conical pile. If the height of the pile is…

A:

Q: Suppose the edges of a cube are increasing at a constant rate of 8 m/hr. Then, the volume of the…

A:

Q: How fast is the volume of a parallelepiped increasing if the length, width, and height of the…

A:

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: The radius of a right circular cone is increasing at a rate of 1.2 in/s while its height is…

A: Differentiate volume wrt t

Q: 2. A water tank is in the form of an inverted right circular cone h feet deep and d feet wide across…

A:

Q: A cube has sides that are increasing at a rate of 10 cm/s. At what rate is the volume increasing…

A: Valur=?

Q: There is a constant outflow of a liquid into a inverted conical vessel 15 m deep and 7.5 m in…

A: Find the rate of change of volume of water in the cone, with respect to time:…

Q: The length of the rectangle is increasing at a rate of 5 cm per second, and its width is decreasing…

A: Area of rectangle = Length * Width

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

Q: A hand-tossed pizza crust starts off as a ball of dough with a volume of 400πcm^3. First, the cook…

A:

Q: Sand is being dumped on a pile in such a way that it always forms a cone whose radius equals to half…

A: Volume of cone: The volume V of cone whose radius is r and height is h is given by, V = 13πr2h.…

Q: Suppose the edges of a cube are increasing at a constant rate of 11 m/hr. Then, the volume of the…

A: Let the side of the cube = x Edges of the cube increasing rate dx/dt = 11 m/hr

Q: A cancer tissue is in the shape of a sphere whose radius is increasing at the rate of 2 mm per day.…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: A block of ice, in the shape of a right circular cone, is melting in such a way that both its height…

A:

Q: 2. A water tank is in the form of an inverted right circular cone h feet deep and d feet wide across…

A: At any time t, let the height of the water be h ft and the radius of the cone formed by the volume…

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: The original 24 m edge length x of a cube decreases at the rate of 3 m/min. a. When x = 4 m, at what…

A:

Q: The length of the rectangle is increasing at a rate of 5 cm per second, and its width is decreasing…

A: Given that, Let length of the ractangle is L and the width is W and area is A. Then according to the…

Q: hypothetical cube shrinks so that the length of its sides are decreasing at a rate of 3 ft/min. At…

A: we have to find

Q: Suppose a liquid is to be cleared of sediment by pouring it through a cone-shaped filter. Assume…

A:

Q: The length of the rectangle is increasing at a rate of 5 cm per second, and its width is decreasing…

A:

Q: 3.) A conical tank is 10ft across the top and 12 ft. deep. If oil is poured into the tank at the…

A:

Q: Water is being poured at the rate of 27 m²/min. into an inverted conical tank that is 12-meter deep…

A:

Q: A liquid solution is passing thru a conical filter 2 feet deep and 4/3 feet across the top, into a…

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

Q: A perfectly spherical balloon is losing volume at a rate of 3 in3 per sec. How fast is the balloon’s…

A:

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 cm/min.…

A:

Q: The original 24 m edge length x of a cube decreases at the rate of 2 m/min. a. When x = 1 m, at what…

A:

Q: 17. If the radius of a sphere is increasing at the constant rate of 3 inches per second, how fast is…

A: Given: The radius of the sphere is increasing at the constant rate of 3 inches per second. To find:…

Q: A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.2 cm/min.…

A:

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

Q: D. Supposes a circle is expanding in such a way that its radius is growing at a constant rate of 3…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 3. The volume of a cube is increasing at the rate of 6 cm³/min. How fast is the surface increasing…

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: 11. At what rate is the volume of the cube changing if the edge is 8 cm and is changing at 4 cm/s?

A: As we know that; The expression for the volume of the cube with the edge length ''a'' is: v=a3…

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.…

Q: Initially filled with water, a conical reservoir is 24 ft deep and 12 ft across the top. Water goose…

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

Q: 1. A spherical balloon is expanding. If the radius is increasing at the rate of 2 inches per minute,…

A: The given question can be solved as shown in step2.

Q: A trough 21m long has ends shaped like isosceles triangles, with base 5m and height 14m. Water is…

A:

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…

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

A:

Q: The length of the rectangle is decreasing at a rate of 5 cm per second, and its width is increasing…

A:

Q: 1. A 50-cm high trough filled with liquid is 200 cm long and has a cross-section of an isosceles…

A: As per our guidelines we are supposed to answer only one question. I am solving the first one Kindly…

Q: A triangle has a base that is decreasing at a rate of 4 cm/s with the height being held constant.…

A: Let b and h be the base and height of the trianglegiven rate at which base is decreasing, dbdt=4cm/s…

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

A:

Q: If the original 24 m edge length x of a cube decreases at the rate of5 m/min, when x = 3 m at what…

A: If the original 24 m edge length x of a cube decreases at the rate of5 m/min, when x = 3 m at what…

Q: The radius of a right circulare cylinder is increasing at the rate of 3 in/sec, while the height is…

A: To determine the change of rate of the volume of cylinder.

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: 5) If the radius of a right circular cylinder is increasing at a rate of 1 inch per minute, and the…

A: The volume of cylinder is given by the formula V=πr2h. The given values are as follows: r=40 inches,…

Q: 4. A trough filled with liquid is 2 m long and has a cross section of an isosceles trapezoid 30 cm…

A: Given: 4) Question is wrong (Some values are missed) 5) dxdt=10 ft/sec, h=100 ft, and l=125 ft