Topic 4.4 Related Rates Check

Which equation is correct for this situation?

The area of a circle is increasing at a rate of 3 inches squared per second.

• $A=3$

• $\frac{dA}{dr}=3$

• $\frac{dA}{dt}=3$

• $\frac{dA}{dt}=3^2$

Which equation is correct for this situation?

A spherical balloon is deflating so that the radius of the balloon is decreasing at a rate of 2cm per second

•  $r=2$ 

•  $\frac{dt}{dr}=-2$ 

•  $\frac{dr}{dt}=2$ 

•  $\frac{dr}{dt}=-2$ 

Which equation is correct for this situation?

Water is being poured into a cylindrical container at the rate of 10 liters per minute. (recall  $V=\pi r^2h$ )

•  $\frac{dr}{dt}=10$ 

•  $\frac{dV}{dt}=10$ 

•  $\frac{dh}{dt}=10$ 

•  $V=1000$ 

Which equation is correct for this situation?

Grain is sitting in a container that is conical in shape.  The bottom of the container has a valve that allows the grain to pour out of the container.  As grain pours out of the container, the height of the grain that remains in the container is decreasing at a rate of 4 feet per minute. (recall  $V=\frac{1}{3}\pi r^2h$ )

•  $\frac{dh}{dt}=-4$ 

•  $\frac{dh}{dt}=4$ 

•  $\frac{dV}{dt}=-4$ 

•  $\frac{dh}{dV}=-4$ 

Which equation is correct for this situation?

The number of Hamburgers H sold in a small town is related to the population p of the town.  The population of the town is growing at the rate of 70 people per year.

•  $\frac{dH}{dp}=70$ 

•  $\frac{dH}{dt}=70$ 

•  $\frac{dp}{dH}=70$ 

•  $\frac{dp}{dt}=70$ 

For each situation below, which units could be used?

Water is being poured into a container. Find the rate that the volume of water in the container is increasing.

• in/minute

• $cm^2$ per second

• $\frac{ft^3}{hour}$

• ft per minute cubed

For each situation below, which units could be used?

The radius of a circle is decreasing.  Find the rate that the circumference of the circle is changing.

• in/minute

• $cm^2$ per second

• $\frac{ft^3}{hour}$

•  $ft^2$ per inch 

For each situation below, which units could be used?

A person is walking away from a light pole.  Find the rate that the length of their shadow is increasing when they are 28 feet from the pole.

• ft/sec

•  $ft^2$ per second

•  $ft^3$ /second

• ft per $\sec^2$ 

For each situation below, which units could be used?

A large tanker inadvertently leaks a large amount of oil while transporting it across water.  Find the rate the surface area of the oil spill is growing.

•  $\frac{m}{\sec^2}$  
  

•  $m^2$ per second

•  $m^3$ /second

•  $m^2$ per seconds squared

For each situation below, which units could be used?

Two planes are flying.  Find the rate that the distance between the planes is changing when they are 120 miles apart.

•  $\frac{mi^2}{hour}$  
  

• hours per mile

• miles per hour per hour

• ft per second