What is the formula for the volume and surface area of a sphere?

What is the formula for the volume and surface area of a sphere?

• A. (4/3) pi (r^3), 4(pi)r^2
• B. 4/3pi r^2, 2(pi)r
• C. pi r^3, 4(pi)r
• D. 2/3pi r^3, 4pi r

Answer: (A)

The volume and surface area of a sphere are fundamental concepts in geometry, and the correct formula for the volume of a sphere is indeed (4/3)πr³, where r represents the radius of the sphere. This formula derives from integral calculus and provides the total space that the sphere occupies. The surface area of a sphere is given by the formula 4πr². This indicates how much area covers the outer surface of the sphere and is critical in many applications, from physics to engineering. The formulas work effectively together to give a complete understanding of the geometric properties of a sphere. Correctly identifying these formulas is essential not just for passing exams like the TExES Mathematics 4-8, but also for practical applications in various scientific and mathematical fields.

The volume and surface area of a sphere are fundamental concepts in geometry, and the correct formula for the volume of a sphere is indeed (4/3)πr³, where r represents the radius of the sphere. This formula derives from integral calculus and provides the total space that the sphere occupies.

The surface area of a sphere is given by the formula 4πr². This indicates how much area covers the outer surface of the sphere and is critical in many applications, from physics to engineering.

The formulas work effectively together to give a complete understanding of the geometric properties of a sphere. Correctly identifying these formulas is essential not just for passing exams like the TExES Mathematics 4-8, but also for practical applications in various scientific and mathematical fields.