math

posted by .

suppose you are drinking root beer from a conical cup. the cup has a diameter of 8 cm and a depth of 10 cm. as you suck the straw, root beer leaves the cup at the rate of 7 cm^3/second. at what rate is the level of the liquid in the cup changng when the liquid is 6 cm deep?

• math -

rate of change of volume = surface area * rate of change of depth
(look at thin slice of area pi r^2 and depth delta h)

what is r?
4/10 = r/6 similar triangles
r = 12/5
surface area = pi(144/25)
so
-7 cm^3/s = pi(144/25) cm^2 * dh/dt
so
dh/dt = -(25*7)/(144 pi) cm/s

Similar Questions

1. Economics

Pat and Kris are roommates. They spend most of their time studying, but they leave some time for their favorite activities: making pizza and brewing root beer. Pat takes 4 hours to brew a gallon of root beer and 2 hours to make a pizza. …
2. Calculus

A leaky cylindrical oilcan has a diameter of 4 inches and a height of 6 inches. The can is full of oil and is leaking at the rate of 2 cubic inches/hr. The oil leaks into an empty conical cup with a diameter of 8 inches and a height …
3. calculus ( related rates )

a paper cup in the shape of a cone has a diameter of 10cm across the top, and is 8cm deep. if the cup is leaking out the bottom at 2pi cm^3/min, at what rate is thet area of the water surface ( only the top surface of the water) changing, …
4. calculus

water is poured into a conical paper cup so that the height increases at the constant rate of 1 inch per second. if the cup is 6 inches tall and its top has a radius of 2 inches, how fast is the volume of water in the cup increasing …
5. Math 2

Cheiko bottles 4 1/8 quarts of root beer. Then she bottles another 5 7/8 quarts of root beer. How many 1-cup servings of root beer does she have?
6. Physics

Suppose you have a very long straw that can reach from a cup of water on the ground level to the top of a very tall building. When you use a pump to suck on the straw in order to bring water up, a. you can bring the water up to any …
7. Physics

Suppose you have a very long straw that can reach from a cup of water on the ground level to the top of a very tall building. When you use a pump to suck on the straw in order to bring water up, a. you can bring the water up to any …
8. Math

a cylindrical cup is made so that the sum of its diameter and its height is 25 cm. find the dimensions of the cup so that the surface area of the cup is a maximum. The answers are. D= 50/3. H=25/3. But how do u get that
9. math

To meke a batch of sugar cookies , you need 0.75 cup of sugar and 1/3 cup of butter , among other ingredients. How much more sugar do you need that butter?
10. math

Water is being poured into a conical cup that is 12cm tall. a) When the water in the cup is 9cm deep, what percentage of the cup is filled?

More Similar Questions