Question

A tank is in the form of an inverted right circular cone. The tank has a height of 4 feet and width of 2 feet. The tank is filled with x inches of water. (a) find an expression for the volume of water in the tank in terms of x, the depth of the water

Answer 1

do u know volume of a cone?

Answer 2

(1/3)(pi)(r^2)h

Answer 3

So this is V, our volume. Which of the variables you have here could represent the height of the water in this cone?

Answer 4

4

Answer 5

I'm looking for on of the variables you have in the formula for volume. It's going to be r or h.

Answer 6

h

Answer 7

*one

Answer 8

right, so now you have volume and you can replace h with x now and you will have volume in terms of x, the height of water in your cone

Answer 9

so x would be (1/3)pi ?

Answer 10

1/3)(pi)(r^2)\(\bf x\)

Answer 11

so it would be x=(1/3)(pi)(1^2)

Answer 12

It would be, since you know r=12 inches, Volume = \(\Large \dfrac 1 3 \pi 12^2 x=\dfrac {144} {3} \pi x\). The fact that the cone is 4 feet tall is irrelevant.

Answer 13

This is volume of water in terms of water height "x" in inches. Volume is in cubic inches.

Answer 14

so the answer is x= 478 inches^3

Answer 15

No. The answer is \(\Large \dfrac {144} {3} \pi x\). This is the volume of water in the cone as a function of x. "x" is a variable. When the amount of water (i.e. volume) in the cone changes, the height of water in the cone (x) will also change. There is no numeric answer unless you wanted to know the volume of water at a certain water level. Now if you plug in 4 ft (48 inches), you'll have the volume of water in the cone at full capacity.

Answer 16

They want an expression, not a numeric answer.

Answer 17

oohhh got it. so if it says the cone is filled with 20 inches of water, i plug 20 inches as x?

Answer 18

you got it!

Answer 19

thank you so much!

Answer 20

my pleasure