If a cylinder with a 4 inch diameter and a 6 inch height holds 1 pound of oatmeal. How much oatmeal will a cylinder (similar) with a 10 inch diameter hold?
Volume of 4 in-----24pi
volume of 10 in----137pi
I get 91 oz
choiced are37,44,74, 192
ddidn't help at all idiot
74
Well, it seems like you've already done the calculations and determined that the volume of the cylinder with a 10 inch diameter is 137pi.
But since you mentioned oatmeal, I have to wonder, are we talking about regular oatmeal or magical expanding oatmeal? Because if it's the latter, then the cylinder could hold an unlimited amount of oatmeal and we might have a bit of a mess on our hands!
But assuming it's regular oatmeal, I think you made a calculation error when converting the volume to ounces. So let's think about this logically.
If the cylinder with a 4 inch diameter holds 1 pound of oatmeal, and the volume of the larger cylinder is more than 1 pound, then we know that the answer cannot be 37, 44, or 74 ounces.
So, the only logical choice left is 192 ounces. Although, that does sound like an awful lot of oatmeal! Perhaps you're planning a really big breakfast party or maybe you're training for an oatmeal-eating competition. In any case, enjoy your oatmeal extravaganza!
To find out how much oatmeal a cylinder with a 10-inch diameter can hold, we can use the concept of similar cylinders. The volumes of similar cylinders are directly proportional to the cube of their corresponding diameters.
First, let's find the volume of the cylinder with a 4-inch diameter. The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
Given that the diameter is 4 inches, the radius (r) would be half of that, which is 2 inches.
Using the formula, we can calculate the volume of the cylinder:
V = π(2^2)(6)
V = 4π(6)
V = 24π cubic inches
Now, let's find the volume of the cylinder with a 10-inch diameter. Again, we need to find the radius first. The radius would be half of the diameter, which is 5 inches.
Using the formula, we can calculate the volume of this cylinder:
V = π(5^2)(h)
V = 25π(h)
Since we know that the volume of the 4-inch cylinder is 24π cubic inches, we can set up a proportion:
(24π) / (24) = (25π)(h) / (25)
Simplifying the equation:
1 = (h) / (25)
h = 25
So, the height of the 10-inch cylinder would be 25 inches.
Now, we can find the volume of the 10-inch cylinder:
V = π(5^2)(25)
V = 25π(25)
V = 625π cubic inches
However, the answer choices are in ounces, not cubic inches. To convert the volume from cubic inches to ounces, we need to consider the density of the oatmeal. The given information states that 1 pound of oatmeal fills the 4-inch cylinder.
1 pound is equal to 16 ounces. So, the volume of oatmeal in the 4-inch cylinder is 16 ounces.
Now, we can set up a proportion to find the volume of oatmeal in the 10-inch cylinder:
16 ounces / 24π = x ounces / 625π
To solve for x:
16/(24π) = x/(625π)
x = (16/24) * 625
x = 10.4 ounces
Therefore, a cylinder with a 10-inch diameter would hold approximately 10.4 ounces of oatmeal. None of the given answer choices match the calculated value, so it seems there might be a discrepancy or mistake in the options provided.
it does
If the cylinders are similar, then the ratio of volumes is (10/4)^3 as much, or 15.625 lbs = 250 oz
how did you get 137pi?
I suspect something is left unsaid here, as none of the choices seems right.