# Using Implicit Differentiation to Solve Related Rates Problems - Page 4

Questions

- A piston is connected by a rod of #14 cm# to a crankshaft at a point #5 cm# away from the axis of rotation. Determine how fast the crankshaft is rotating when the piston is 11 cm away from the axis of rotation and is moving toward it at 1200 cm/s?
- Anna is 6 ft. tall. She is walking away from a street light that is 24 ft tall at a rate of 4 ft/sec. How fast is the length of her shadow changing?
- Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 4 cm/min. How fast is the area of the pool increasing when the radius is 5 cm?
- A hypothetical square grows so that the length of its diagonals are increasing at a rate of 4 m/min. How fast is the area of the square increasing when the diagonals are 14 m each?
- A conical paper cup is 10 cm tall with a radius of 30 cm. The cup is being filled with water so that the water level rises at a rate of 2 cm/sec. At what rate is water being poured into the cup when the water level is 9 cm?
- A conical paper cup is 10 cm tall with a radius of 10 cm. The cup is being filled with water so that the water level rises at a rate of 2 cm/sec. At what rate is water being poured into the cup when the water level is 8 cm?
- Water is being drained from a cone-shaped reservoir 10 ft. in diameter and 10 ft. deep at a constant rate of 3 ft3/min. How fast is the water level falling when the depth of the water is 6 ft?
- Water is being pumped into a vertical cylinder of radius 5 meters and height 20 meters at a rate of 3 meters/min. How fast is the water level rising when the cylinder is half full?
- A spherical balloon is being inflated at the rate of 12 cubic feet per second. What is the radius of the balloon when its surface area is increasing at a rate of 8 feet square feet per second? Volume= (4/3)(pi)r^3 Area= 4(pi)r^2?
- A perfect cube shaped ice cube melts so that the length of its sides are decreasing at a rate of 2 mm/sec. Assume that the block retains its cube shape as it melts. At what rate is the volume of the ice cube changing when the sides are 2 mm each?
- A street light is at the top of a 12 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 5 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 45 ft from the base of the pole?
- A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 ft/sec. Assume the scenario can be modeled with right triangles. At what rate is the length of the person's shadow changing when the person is 16 ft from the lamppost?
- What is the rate of change of the width (in ft/sec) when the height is 10 feet, if the height is decreasing at that moment at the rate of 1 ft/sec.A rectangle has both a changing height and a changing width, but the height and width change so that the area of the rectangle is always 60 square feet?
- Water is leaking out of an inverted conical tank at a rate of 10,000 cm3/min at the same time water is being pumped into the tank at a constant rate If the tank has a height of 6m and the diameter at the top is 4 m and if the water level is rising at a rate of 20 cm/min when the height of the water is 2m, how do you find the rate at which the water is being pumped into the tank?
- Help with a related rates problem?
- A right cylindrical water tank with a diameter of 3 feet and a height of 6 feet is being drained. At what rate is the volume of the water in the tank changing when the water level of the tank is dropping at a rate of 4 inches per minute?
- How fast is the radius changing when diameter of the snowball is 10 cm given a spherical snowball with an outer layer of ice melts so that the volume of the snowball decreases at a rate of 2cm per 3min?
- What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building if an 8ft fence runs parallel to a tall building at the distance of 4ft from the building?
- If the rate of change in #x# is #"3 s"^(-1)#, and #(dy)/(dx) = 5#, what is the rate of change in #y#? Is #y# changing faster than #x# or vice versa?
- A street light is at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 8 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 35 ft from the base of the pole?