Katie Calculus Pumpkin Balloon Related Rates

As Katie leaves the cemetery, she notices a giant spherical pumpkin balloon. She notices (with her calibrated eyeball) it has a volume of $$36\pi\ ft^3$$  . She also noticed the volume is being increased at a rate of $$2\frac{ft^3}{\sec}$$  .How fast is the radius of the balloon changing?

Part 1:

What are you trying to find?

As Katie leaves the cemetery, she notices a giant spherical pumpkin balloon. She notices (with her calibrated eyeball) it has a volume of $$36\pi\ ft^3$$  . She also noticed the volume is being increased at a rate of $$2\frac{ft^3}{\sec}$$  .How fast is the radius of the balloon changing? Select all that apply.

Part 2:

What is given in the original problem?

As Katie leaves the cemetery, she notices a giant spherical pumpkin balloon. She notices (with her calibrated eyeball) it has a volume of $$36\pi\ ft^3$$  . She also noticed the volume is being increased at a rate of $$2\frac{ft^3}{\sec}$$  .How fast is the radius of the balloon changing?

Part 3:

What equation will relate the radius to the volume?

As Katie leaves the cemetery, she notices a giant spherical pumpkin balloon. She notices (with her calibrated eyeball) it has a volume of $$36\pi\ ft^3$$  . She also noticed the volume is being increased at a rate of $$2\frac{ft^3}{\sec}$$  .How fast is the radius of the balloon changing?

Part 4:

Find the radius at the given volume.

As Katie leaves the cemetery, she notices a giant spherical pumpkin balloon. She notices (with her calibrated eyeball) it has a volume of $$36\pi\ ft^3$$  . She also noticed the volume is being increased at a rate of $$2\frac{ft^3}{\sec}$$  .How fast is the radius of the balloon changing?

Part 5:

Find the Find the derivative of the volume equation with respect to time.

As Katie leaves the cemetery, she notices a giant spherical pumpkin balloon. She notices (with her calibrated eyeball) it has a volume of $$36\pi\ ft^3$$  . She also noticed the volume is being increased at a rate of $$2\frac{ft^3}{\sec}$$  .How fast is the radius of the balloon changing?

Part 6:

How fast is the radius changing? Select all acceptable answers for the College Board.

As Katie leaves the cemetery, she notices a giant spherical pumpkin balloon. She notices (with her calibrated eyeball) it has a volume of $$36\pi\ ft^3$$  . She also noticed the volume is being increased at a rate of $$2\frac{ft^3}{\sec}$$  .How fast is the radius of the balloon changing?

Part 7:

What are the units