A pool shaped like the bottom half of a sphere is being filled at a rate of 28 cubic feet per min...
Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a constant rate of 9 cubic feet per minute. If the pool has radius 3 feet and height 11 feet, what is the rate of change of the height of the water in the pool when the depth of the water in the pool is 9 feet?
8. A conical storage tank is being filled at a rate of 60 ft./minute. If the top of the tank is 10 feet in diameter and the depth is 50 feet, at what rate is the radius changing after 3 minutes? V = 1/3 Tr?h. (6 points)
show work 4. The spherical balloon is being filled with water at a rate of 25 cm/min. At what rate if the radius 4 changing when the radius is 4 cm? (Volume of a sphere: V =
4. A spherical balloon is inflated at a rate of 10 cubic feet per minute. How fast is the radius changing when the radius is 2 ft? (V = far)
A swimming pool is 40 feet long, 20 feet wide, 8 feet deep at the deep end, and 3 feet deep at the shallow end; the bottom is rectangular. If the pool is filled by pumping water into it at the rate of 40 cubic feet per minute, how fast is the water level rising when it is 3 feet deep at the deep end?
Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter is alwaysequal to its height. How fast is the height of the pile increasing when the pile is 18 feet high? Recall that the volume of a right circular cone with height h andradius of the base r is given by V=1/3*pi*r^2*hWhat isr requested rate of increase of...
6. (6 pts) An expandable sphere is being filled with liquid at a constant rate from a tap (imagine a water balloon connected to a faucet). When the radius of the sphere is 3 inches, the radius is increasing at 2 inches per minute. How fast is the liquid coming out of the tap? (Volume of a sphere = ar") Use appropriate units in your answer.
Gravel is being dumped from a conveyor belt at a rate of 20 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 19 feet high? Recall that the volume of a right circular cone with height h and radius of the base r is given by v= 1/3pi(r)^2hokay so this is...
There is water being taken/pumped out of a swimming pool that it round. The pool has a radius of R= 2.52m and it currently filled to a depth of ha=3.52m. The drain hose has a radius of rc=0.0316m. The height of the water at point A is slowly decreasing at a rate of 6.18cm/per minute. What us the velocity of the water through the drainpipe Vc=? What is the height hd of the water in the vertical tube, while the...
A spherical balloon is inflated with gas at a rate of 900 cubic centimeters per minute. (a) Find the rates of change of the radius when r = 40 centimeters and r = 75 centimeters. r = 40 cm/min r = 75 cm/min (b) Explain why the rate of change of the radius of the sphere is not constant even though dV/dt is constant. The rate of change of the radius is a linear relationship whose slope is dV dt...