How To Calculate The Radius of a Sphere Given The Volume | Summary and Q&A

TL;DR

This video explains how to calculate the radius of a sphere using the volume, providing step-by-step instructions and examples.

Key Insights

• 🔇 A sphere's volume can be calculated using the formula V = (4/3)πr^3.
• 😀 To find the radius, rearrange the formula as R = (3V/4π)^(1/3).
• 🇦🇪 The unit of the radius depends on the unit used in the volume calculation.
• 🧑‍🏭 Conversion factors can be used to convert the radius from one unit to another.
• 🧊 The cube root of a unit cubed simplifies to just the unit itself.
• 🥇 Placing parentheses around the exact value of π is important to ensure accurate calculations.
• 🔇 Calculating the radius of a sphere requires the volume and the formula R = (3V/4π)^(1/3).

Transcript

Read and summarize the transcript of this video on Glasp Reader (beta).

Questions & Answers

Q: What is the formula for finding the volume of a sphere?

The formula for finding the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius.

Q: How can we find the radius of a sphere using the given volume?

To find the radius, rearrange the volume formula as R = (3V/4π)^(1/3) and substitute the given volume into the equation.

Q: Can you provide an example of calculating the radius using volume?

Sure! For example, if the volume is 4189, you can use the formula R = (3 * 4189 / (4 * π))^(1/3). After solving, the radius is approximately 10 centimeters.

Q: How do we convert the radius from one unit to another?

To convert the radius from one unit to another, such as from feet to inches, you need to multiply the length in the original unit by the appropriate conversion factor. For example, if the radius is 2.5 feet, you can convert it to inches by multiplying 2.5 by 12, resulting in a radius of 30 inches.

Summary & Key Takeaways

• The formula for calculating the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius.

• To find the radius, rearrange the formula as R = (3V/4π)^(1/3) and plug in the given volume.

• Example 1: Given a volume of 4189, the radius is approximately 10 centimeters.

• Example 2: Given a volume of 65.45 cubic feet, the radius is approximately 30 inches.