If a can of ravioli with a diameter of 2 inches and a height of 4.5 inches holds 12 ounces of ravioli, how many ounces of ravioli would a can with the same height, but double the diameter, hold?
Four times as much:
volume of 1st can = π(1^2 (4.5) = 4.5π
volume of 2nd can = π(2^2)(4.5)= 18π
and 18π = 4 ( 4.5π)
so it would hold 48 ounces
blah blah
To find out how many ounces of ravioli a can with double the diameter would hold, we can use the concept of volume.
First, let's calculate the volume of the original can using the formula for the volume of a cylinder: V = πr^2h, where V is the volume, r is the radius, and h is the height.
Given that the diameter is 2 inches, the radius (r) would be half of that, which is 1 inch. And the height (h) is 4.5 inches.
So, the volume of the original can is V = π(1^2)(4.5) = 4.5π cubic inches.
Now, let's calculate the volume of the can with double the diameter. The new diameter would be 2 * 2 = 4 inches, and the height remains the same at 4.5 inches.
Using the same formula, the volume of the new can would be V = π(2^2)(4.5) = 18π cubic inches.
Finally, we need to relate the volume of the cans to the amount of ravioli they can hold. Given that the original can holds 12 ounces of ravioli, we need to calculate the ratio of the volumes.
The ratio of the volumes is (18π cubic inches) / (4.5π cubic inches) = 4.
Since the volumes are proportional to the amount of ravioli, we can conclude that a can with double the diameter would hold 4 times the amount of ravioli as the original can.
Therefore, the can with double the diameter would hold 12 ounces * 4 = 48 ounces of ravioli.