How to Calculate Volume and Surface Area of a Sphere

TL;DR

To calculate the volume of a sphere, use the formula V = 4/3πr³, where r is the radius. For the surface area, the formula is A = 4πr². To find the radius from the volume or the diameter from the surface area, rearrange these formulas as needed.

Transcript

in this video we're going to talk about how to find the volume of a sphere and the surface area of a sphere so let's talk about the volume first let's say i know this looks like a circle but treat it as a sphere so let's say if we have a sphere with radius r to find the volume of the sphere it's four thirds pi r cube and to calculate the surface ar... Read More

Key Insights

• 🔇 The volume of a sphere is given by V = 4/3πr³, where r is the radius.
• 😀 The surface area of a sphere is given by A = 4πr², where r is the radius.
• 🔇 The formulas for volume and surface area of a sphere are essential in solving problems involving spheres.
• 🔇 If the radius is known, the volume and surface area of a sphere can be easily calculated using the respective formulas.
• 🔇 To find the radius given the volume of a sphere, the formula V = 4/3πr³ can be rearranged and solved.
• ❓ The diameter of a sphere is twice the length of its radius.
• ❎ The surface area of a sphere is always measured in square units.

Questions & Answers

Q: How do you calculate the volume of a sphere?

The volume of a sphere can be found using the formula V = 4/3πr³, where r is the radius. Simply substitute the radius value into the formula and calculate.

Q: How do you calculate the surface area of a sphere?

The surface area of a sphere can be calculated using the formula A = 4πr², where r is the radius. Plug in the radius value and compute the result.

Q: How do you find the radius of a sphere given its volume?

To find the radius of a sphere when its volume is known, rearrange the formula V = 4/3πr³ to solve for r. Substitute the volume value and solve for r using appropriate mathematical operations.

Q: How do you find the diameter of a sphere with a given surface area?

First, find the radius of the sphere using the formula A = 4πr². Once you have the radius, simply double it to find the diameter, as diameter = 2r.

Summary & Key Takeaways

• The volume of a sphere can be calculated using the formula: V = 4/3πr³, where r is the radius.

• The surface area of a sphere can be calculated using the formula: A = 4πr², where r is the radius.

• To find the radius of a sphere given its volume, the equation V = 4/3πr³ can be rearranged to solve for r.

• To find the diameter of a sphere given its surface area, the equation A = 4πr² can be used to find the radius, and then the diameter can be calculated as 2r.