if there are 2 cylindrical cans. A label on the small one says it has a volume of 513 grams. the large one was destroyed. the small can's diameter was the same as the large can. large was 1/3 taller than the small can. what is the volume of the large can?
If the diameters are the same, the volume is proportional to length.
A gram is not a measure of volume.
The larger can is 4/3 times larger than the small can, and contains 684 g.
To find the volume of the large can, we'll need to use the information given and make some calculations.
Let's assign variables to the dimensions of the small can:
- Diameter of the small can: d
- Height of the small can: h
We know that the label on the small can says it has a volume of 513 grams. However, volume is typically measured in cubic units (like cubic centimeters or cubic inches), not grams. So, it seems that there might be a mistake in the information provided.
Assuming it's a typo, let's assume the label on the small can actually refers to the volume and not the weight. In that case, we can calculate the volume of the small can. The volume of a cylinder is calculated using the formula V = π * r^2 * h, where r is the radius of the cylinder's base and h is the height.
Since the diameter of the small can is the same as the large can, we can assume the radius of both cans is the same, which is half of the diameter. Therefore, for the small can, the radius is d/2.
Now, we have the following information:
- Volume of the small can = 513 cm³
- The large can is 1/3 taller than the small can, so its height is 3/3 + 1/3 = 4/3 times the height of the small can.
Let's denote the volume of the large can as V_large.
Using the volume formula and the given information, we can set up the following equation:
V_small = π * (d/2)^2 * h
513 = π * (d/2)^2 * h
Now, we need one more piece of information to solve for the volume of the large can. We need either the diameter, height, or volume of the large can. Without that information, we cannot determine the volume of the large can precisely.
If you have any additional details or if there has been any misunderstanding in the given information, please let me know so I can provide a more accurate answer.