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b. The volume of one size can is 350 cubic centimeters. What is the radius of this can? (Type an integer or decimal rounded to the nearest hundredth as needed.) nexample Get more help.

Ask by Williams Li. in the United States
Jan 08,2025

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Answer

To find the radius of the can, you need to know its height. The radius can be calculated using the formula \( r = \sqrt{\frac{V}{\pi h}} \), where \( V \) is the volume (350 cm³) and \( h \) is the height. Without the height, the radius cannot be determined.

Solution

To determine the radius of the can given its volume, we'll assume the can is a **cylindrical** shape. The formula for the volume \( V \) of a cylinder is: \[ V = \pi r^2 h \] Where: - \( V \) is the volume, - \( r \) is the radius, - \( h \) is the height. However, to solve for the radius \( r \), **we need to know the height** of the can. Since the height isn't provided in your question, I'll outline the steps assuming you have that information. ### Steps to Calculate the Radius: 1. **Identify the Given Values:** - Volume \( V = 350 \) cubic centimeters. - Height \( h \) (you need to provide this value). 2. **Rearrange the Volume Formula to Solve for \( r \):** \[ r = \sqrt{\frac{V}{\pi h}} \] 3. **Plug in the Known Values and Compute:** For example, if the height \( h = 10 \) cm: \[ r = \sqrt{\frac{350}{\pi \times 10}} = \sqrt{\frac{350}{31.4159}} \approx \sqrt{11.14} \approx 3.34 \text{ cm} \] 4. **Round the Answer:** - Round the radius to the nearest hundredth as needed. ### Without the Height: If the can's height isn't provided, it's not possible to accurately determine the radius. Please check if the height is given in another part of the problem or provide it so that the calculation can be completed. ### Example Answer (Assuming Height is 10 cm): \[ r \approx 3.34 \text{ cm} \] *Please replace the height with the appropriate value if it's different.*

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To find the radius of a cylindrical can with a volume of 350 cubic centimeters, you can use the formula for the volume of a cylinder: V = πr²h, where V is volume, r is radius, and h is height. However, you need to know the height of the can to find the radius. If you assume a particular height, plug that value into the formula and solve for r. If the height is, say, 10 cm, you'd rearrange to find r = √(V/(πh)), which gives you a clear path to the answer! Cylindrical cans are commonly used in various industries, from food packaging to chemical storage. Understanding their dimensions is crucial not just for packaging but also for optimizing transportation and storage. Knowing the radius helps in calculating how many cans can fit into a certain space or container, ensuring efficiency and reducing waste during shipping and handling!

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