Using Implicit Differentiation to Solve Related Rates Problems - Page 6

Questions
  • There is a square pyramid with its vertex on bottom. Its base is #12# #meters# on each side. Its height is #4# #meters#. It is being filled with water at a rate of #9# #m^3#/#min#. How fast is the depth of the water growing when the depth is #2# #meters#?
  • The radius of a cylinder is decreasing at the rate of 4 ft/min, while the height is increasing at the rate of 2 ft/min. What is the rate of change of the volume when the radius is 2 feet and the height is 6 feet?
  • How to answer these question using differentiation ?
  • A cylindrical jar, of radius 3 cm, contains water to a depth of 5 cm. The water is then poured at a steady rate into an inverted conical container with its axis vertical. ?
  • How fast is the water level rising when the water is 1 foot deep?
  • It's a related rate problem. PLease help ?
  • Water flows on to a flat surface at a rate of 5cm3/s forming a circular puddle 10mm deep. How fast is the radius growing when the radius is? 1cm? 10cm? 100cm?
  • How to solve the following ??
  • What is an appropriate differential equation, and what is the answer for V?
  • A conical water tank with its vertex at bottom has radius 20m and depth 20m.Water is being pumped into the tank at rate 40m^3/min.how fast is the level of the water rising when water is 8m deep? ( v=(pi x r² x h)/3 )
  • A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. Water is flowing into the tank at a rate of 5 cubic feet per minute. Find the rate of change of the depth of the water when the water is 4 feet deep.?
  • Gasoline is pumped from the tank of a tanker truck at a rate of 20L/s. If the tank is a cylinder 2.5m in diameter and 15m long, at what rate is the level of gasoline falling when the gasoline in the tank is 0.5m deep?
  • I'd need help with the whole question..but even just in part 9i, the answer is d(theta)/d(t)=kt. Where does the t come from?? It's simple things like this which confuse me.. Thanks for your help!!
  • How do go about this problem after finding dp/dt in terms of and dV/dt?
  • How fast is the water level rising when the water is 3 cm deep (at its deepest point) if water is poured into a conical container at the rate of 10 cm3/sec. the cone points directly down, and it has a height of 25 cm and a base radius of 15 cm?
  • Water is leaking out of an inverted conical tank at the rate of 10,000cm^3/min cm/min at the same time that water is being pumped into the tank at a constant rate. The tank has a height of 6m and the diameter at the top is 4m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2m, how can I find the rate at which water is being pumped into the tank.?
  • How to solve using derivative??
  • The temperature of a cup of coffee cools from 105 deg to room temperature (20 deg). After 5 mins the temperature is 95 deg. Find (a) formula for the temperature at time t, (b) the temperature after 11 mins c) time for the temperature to drop to 85 deg?
  • How to find the rate at which water is being pumped into the tank in cubic centimeters per minute? details below:
  • I have tried methods but still can't get correct answer, Can give me some helps??