a can of soup completely fills a cylinder 5 inches tall and 3 inches in diameter. If one can of soup is poured into a cylindrical pot with a diameter of 6 inches, to what depth, in inches, will it fill the pot?

is the answer 10?

If you think about it, that won't work logically. Your 2nd pot is wider than your first pot, so it will have to be more shallow to fill the same amount of water.

V= pi x r^2 x h

So the first thing we have to do is figure out the volume of the first cylinder.

Pi = 3.14
The radius is half the diameter. So 1/2 of 3 is 1.5. 1.5 squared is 2.25 inches.
The height is 5 inches.

3.14 x 2.25 x 5

That's 35.325 inch^3

That's how much water we have. Now, we just have to plug that into the same equation for the 2nd thing.

35.325 = 3.14 x 9 x ?

35.325 = 28.26x

So take 35.325 divided by 28.26 and your answer is...

:)

With twice the diameter, the base area is 4 times that of the small, full can. That means the liquid inside the wider can will rise to 1/4 the former height, or 5/4 inch.

This agrees with the previous answer but is easier to calculate.

To find the depth to which the can of soup will fill the pot, we need to calculate the volume of the can and the volume of the pot.

First, let's determine the volume of the can of soup. The can is shaped like a cylinder, and the volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.

Given that the diameter of the can is 3 inches, the radius would be half of that, which is 1.5 inches. The height of the can is given as 5 inches.

Using the formula, we can calculate the volume of the can:

V_can = π * (1.5)^2 * 5
= 3.14 * 2.25 * 5
= 35.32 cubic inches

Now, let's determine the volume of the pot. The pot is also shaped like a cylinder, and the diameter is given as 6 inches. Therefore, the radius would be half of that, which is 3 inches.

Since we don't have the height of the pot, we will use variable 'h' to represent it.

The volume of the pot can be calculated as:

V_pot = π * (3)^2 * h
= 3.14 * 9 * h
= 28.26h cubic inches

We're given that one can of soup is poured into the pot. So, the volume of the can (35.32 cubic inches) will be equal to the volume of the soup in the pot, which is equal to the volume of the pot itself (28.26h).

Now, we can set up an equation to find the depth the soup will fill the pot:

35.32 = 28.26h

To solve for 'h', we divide both sides of the equation by 28.26:

h = 35.32 / 28.26
h ≈ 1.25

Therefore, the soup will fill the pot to a depth of approximately 1.25 inches. So, the answer is not 10 inches; it is approximately 1.25 inches.