A conical tank, point down, has a radius of 6 feet and a depth of 9...

A conical tank, point down, has a radius of 6 feet and a depth of 9 feet. Water is filling the tank and thus the volume of water in the tank is changing with time, as is the depth of the water and the radius of the surface of the water. Suppose that at the instant the depth of the water is 4 feet, the depth of the water is changing at an instantaneous rate of0.125 feet per minute. How fast is the volume of water in the tank changing at that instant?

Expert Solution

Let r be the radius and h be the depth of the conical tank at any time t. Then using the similarity of triangles, we will get a relation between r and h. Applying the formula of the volume of the cone, V, we have to find dV/dt, as explained in the solution provided.

milcah answered 2 years ago

A conical tank has height 9 m and radius 4 m at the base. Water flows...

A conical tank has height 9 m and radius 4 m at the base. Water flows at a rate of 3 m^3/min. How fast is the water level rising when the level is 1 m and 2 m? (Use symbolic notation and fractions where needed.) When the water level is 1 m, the water level is rising at a rate of _ .When the water level is 2 m, the water level is rising at a rate of _.

A spherical ball of radius 3 in is dropped into a conical vessel of depth 8...

A spherical ball of radius 3 in is dropped into a conical vessel of depth 8 in and radius of base 6 in. what is the area of the portion of the sphere which lies above the circle of contact with the cone?

A conical tank extends from two foot in diameter at the discharge to twelve feet in...

A conical tank extends from two foot in diameter at the discharge to twelve feet in diameter at the top with sides 30 degree from the vertical. Water flows into the tank at 100 lbm/min. How long does it take to fil the tank to 80 percent full?

A water tank is spherical in shape with radius of 90 feet. Suppose the tank is...

A water tank is spherical in shape with radius of 90 feet. Suppose the tank is filled to a depth of 140 feet with water. Some of the water will be pumped out and, at the end, the depth of the remaining water must be 40 feet. i) Set up a Riemann sum that approximates the volume of the water that is pumped out of the tank. (use horizontal slicing). You have to draw a diagram and choose a coordinate...

A spherical storage tank contains oil. The tank has a diameter of 6 feet. You are...

A spherical storage tank contains oil. The tank has a diameter of 6 feet. You are asked to calculate the height at which an 8-foot-long dipstick would be wet with oil when immersed in the tank when it contains 6 ft3 of oil. The equation giving the height h of the liquid in the spherical tank for the given volume and radius is given by: f(h) = h3−9h2 + 3.8197 Use the secant method to find roots of equations to...

An underground tank is a hemisphere with radius 4 feet (i.e. it is half a sphere,...

An underground tank is a hemisphere with radius 4 feet (i.e. it is half a sphere, and so horizontal cross-sections are circles of varying radius). It is filled to the top with oil weighing 45 lb per cubic foot. The top of the tank is at ground level, and the oil in the tank is pumped to a height of 10 feet above ground level. How much work is done? Set up the integral, but then just use your calculator...

A Ferris wheel has a radius of 10 feet and is boarded in the 6 o’clock...

A Ferris wheel has a radius of 10 feet and is boarded in the 6 o’clock position from a platform that is 3 feet above the ground. The wheel turns counterclockwise and completes a revolution every 3 minutes. At t = 0 the person is at the 6 o’clock position. 1. Draw a diagram and impose coordinates 2. Find a function, F(t), for the height of the person above the ground after t minutes 3. Find two times when a...

A conical tank of diameter 6 m and height 10 m is filled with water. Compute...

A conical tank of diameter 6 m and height 10 m is filled with water. Compute for the work needed to pump all the water 2 m above the tank. The water has a density of 1000 kg per cubic meter.

The tank in the form of a right-circular cone of radius 7 feet and height 39...

The tank in the form of a right-circular cone of radius 7 feet and height 39 feet standing on its end, vertex down, is leaking through a circular hole of radius 4 inches. Assume the friction coefficient to be c=0.6 and g=32ft/s^2 . Then the equation governing the height h of the leaking water is dhdt=_______________ If the tank is initially full, it will take _________ seconds to empty.

If Dave is standing next to a silo of cross-sectional radius r = 9 feet at...

If Dave is standing next to a silo of cross-sectional radius r = 9 feet at the indicated position, his vision will be partially obstructed. Find the portion of the y-axis that Dave cannot see. (Hint: Let a be the x-coordinate of the point where line of sight #1 is tangent to the silo; compute the slope of the line using two points (the tangent point and (12, 0)). On the other hand, compute the slope of line of sight...

Question