A cylinder with a 4-inch diameter and a 6-inch height folds 1 pound of oatmeal. To the nearest ounce, how much oatmeal will a similar 10-inch cylinder hold? (hint: 1 pound=16 ounces)
37 ounces
44 ounces
74 ounces
192 ounces
We know that the volume of a cylinder is given by the formula V = πr^2h, where V is the volume, r is the radius and h is the height. Let V1 and V2 be the volumes of the two cylinders.
First, we find the volumes of the two cylinders. We are given that the smaller cylinder has a diameter of 4 inches, so its radius is 2 inches, and its height is 6 inches. Thus, V1 = π(2)^2(6) = 24π cubic inches.
The larger cylinder has a diameter of 10 inches, so its radius is 5 inches. We do not know the height of the larger cylinder, but since it is similar to the smaller cylinder, the ratio of their heights is the same as the ratio of their radii, which is 2/5. So, the height of the larger cylinder is 6 * (5/2) = 15 inches.
Now we find the volume of the larger cylinder: V2 = π(5)^2(15) = 375π cubic inches.
Next, we find the ratio of the volumes of the larger and the smaller cylinder: V2/V1 = (375π)/(24π) = 375/24 = 15.625
So, the larger cylinder can hold 15.625 times more oatmeal than the smaller cylinder. Since the smaller cylinder can hold 1 pound of oatmeal, the larger cylinder can hold 15.625 pounds of oatmeal.
To convert this to ounces, we multiply by 16: 15.625 pounds * 16 ounces/pound = 250 ounces.
To the nearest ounce, the larger cylinder can hold 250 ounces of oatmeal. However, since that is not an option, the closest option is 192 ounces.