Question

Gasoline is pouring into a cylindrical tank of radius 4 feet. When the depth of the gasoline is 6 feet, the depth is increasing at .4 ft/sec. How fast is the volume of gasoline changing at that instant?
Round your answer to three decimal places.

Answer 1

20.106

Answer 2

so its this one :)

Answer 3

yes!

Answer 4

does the depth mean volume?

Answer 5

I got no idea if supers answer is correct or not, but only an idiot would accept it without some sort of proof :/

Answer 6

yes, i didn't want the answer but needed help with understanding it thank you >_<

Answer 7

Gasoline is pouring into a cylindrical tank of radius 4 feet.

When the depth of the gasoline is 6 feet,
the depth is increasing at .4 ft/sec.

How fast is the volume of gasoline changing at that instant?

We need a formula for the volume of a cylindar ....

Answer 8

i believe it's V= pie * radius ^2 * h?

Answer 9

correct; but lets rename some parts to match the question; d for depth is good

Answer 10

\[V(d)=pi\ r^2\ d(t)\]
\[V=pi\ 4^2\ d(t)\]
\[V=16pi\ d(t)\]
this should be good for our purposes

Answer 11

in other questions the radius changes as the height or depth thanks to it being a cone shape or some other; but in a cylindar we the radius is constant :)

Answer 12

\[V' = 16pi\ d'(t)\]
since the rate of change of depth is given, we just plug it in

Answer 13

thank you so much got the right answer! you make it sound so easy! sorry to bother you but could you please help me with my other two questions??

Answer 14

do I have to find the distance between 2 points?

Answer 15

i dont think so? A rectangular swimming pool is to be built with an area of 1800 square feet. The owner wants 5-foot wide decks along either side and 10-foot wide decks at the two ends. Find the dimensions of the smallest piece of property on which the pool can be built satisfying these conditions. Give the answers in ascending order