# P16 - Project 16 MAC 2311 YOU MUST SHOW YOUR WORK TO...

This preview shows pages 1–2. Sign up to view the full content.

Project 16 MAC 2311 YOU MUST SHOW YOUR WORK TO RECEIVE FULL CREDIT!! 1. An underwater pipe begins to leak oil that spreads outward in the shape of an expanding sphere. Recall that the volume of a sphere is V = 4 3 πr 3 , where r is the length of its radius. Suppose the company that owns the pipe takes some measurements and discovers that the volume (in cubic feet) of the spill has been V ( t ) = 3 + 2 t + t 2 , where t is the number of hours since the spill began ( t = 0). Calculate dr dV (ﬁrst write r as a function of V ). Write a formula r ( t ) for the radius of the oil spill as a function of t and calculate r 0 ( t ). What does dr dt represent? What are its units? Draw a picture of the situation at the exact moment when t = 4 labelling the numerical values of the radius and volume of the sphere. At what rates are the volume and the radius of the spill changing at that time? At what rates are they changing after 100 hours? Include the units with your answers and round to the nearest hundredth. Show that as time passes, the radius of the spill will extend outward without

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

P16 - Project 16 MAC 2311 YOU MUST SHOW YOUR WORK TO...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online