# Using Implicit Differentiation to Solve Related Rates Problems - Page 3

Questions

- A girl of height 120 cm is walking towards a light on the ground at a speed of 0.6 m/s. Her shadow is being cast on a wall behind her that is 5 m from the light. How is the size of her shadow changing when she is 1.5 m from the light?
- Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The area of the spill increases at a rate of 9π m²/min. How fast is the radius of the spill increasing when the radius is 10 m?
- How do you find the rate at which a batter's distance from second base decreases when he is halfway to first base if the baseball diamond is a square with side 90 ft and a batter hits the ball and runs toward first base with a speed of 24 ft/s?
- Water is pouring into a cylindrical bowl of height 10 ft. and radius 3 ft, at a rate of #5" ft"^3/"min"#. At what rate does the level of the water rise?
- The radius of a spherical balloon is increasing at a rate of 2 centimeters per minute. How fast is the volume changing when the radius is 14 centimeters?
- A six foot tall person is walking away from a 14 foot tall lamp post at 3 feet per second. When the person is 10 feet from the lamp post, how fast is the tip of the shadow moving away from the lamp post?
- How do you determine what percentage of chlorine is in the pool after 1 hour if a pool whose volume is 10000 gallons contains water the is 0.01%chlorine and starting at t=0 city water containing .001% chlorine is pumped into the pool at a rate of 5 gal/min while the pool water flows out at the same rate?
- The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3 cm/s. When the length is 20 cm and the width is 10 cm, how fast is the area of the rectangle increasing?
- A hypothetical cube shrinks at a rate of 8 m³/min. At what rate are the sides of the cube changing when the sides are 3 m each?
- A street light is mounted at the top of a 15ft tall pole. A man 6ft tall walks away from the pole with a speed of 5ft/sec along a straight path. How fast is the tip of his shadow moving when he is 40ft from the pole?
- A ferris wheel with a radius of 10 m is rotating at a rate of one revolution every 2 minutes How fast is a rider rising when the rider is 16 m above ground level?
- A feeding trough full of water is 5 ft long and its ends are isosceles triangles having a base and height of 3 ft. Water leaks out of the tank at a rate of 5 (ft)^3/min. How fast is the water level falling when the water in the tank is 6 in. deep?
- How do you find the amount of sugar in the tank after t minutes if a tank contains 1640 liters of pure water and a solution that contains 0.09 kg of sugar per liter enters a tank at the rate 5 l/min the solution is mixed and drains from the tank at the same rate?
- A hypothetical square grows at a rate of 16 m²/min. How fast are the sides of the square increasing when the sides are 15 m each?
- How do you determine how much salt is in the tank when it is full if a 30-gallon tank initially contains 15 gallons of salt water containing 5 pounds of salt and suppose salt water containing 1 pound of salt per gallon is pumped into the top of the tank at the rate of 2 gallons per minute, while a well-mixed solution leaves the bottom of the tank at a rate of 1 gallon per minute?
- If the radius of a sphere is increasing at a rate of 4 cm per second, how fast is the volume increasing when the diameter is 80 cm?
- A square is inscribed in a circle. How fast is the area of the square changing when the area of the circle is increasing at the rate of 1 inch squared per minute?
- At what approximate rate (in cubic meters per minute) is the volume of a sphere changing at the instant when the surface area is 5 square meters and the radius is increasing at the rate of 1/3 meters per minute?
- Water leaking onto a floor forms a circular pool. The area of the pool increases at a rate of 25π cm²/min. How fast is the radius of the pool increasing when the radius is 6 cm?
- How do you find the rate at which the volume of a cone changes with the radius is 40 inches and the height is 40 inches, where the radius of a right circular cone is increasing at a rate of 3 inches per second and its height is decreasing at a rate of 2inches per second?