Cylinders, Cones and Spheres: Calculating the surface area of a sphere

The video tutorial explains the concept of a sphere and its surface area. It introduces the formula for the surface area of a sphere, which is 4πR², and discusses its derivation using calculus. The tutorial provides two examples to demonstrate how to calculate the surface area: one with a radius in meters and another with a radius in inches. The importance of understanding units and the concept of square units in area calculations is emphasized.

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

• πR²

• 4πR²

• 2πR²

• 3πR²

Why is the factor of 4 included in the surface area formula of a sphere?

• To adjust for the circular nature of the sphere

• To account for the volume of the sphere

• To simplify the calculation

• To cover the entire surface area

Which mathematical field is necessary to derive the surface area formula of a sphere?

• Algebra

• Geometry

• Trigonometry

• Calculus

If a sphere has a radius of 7 meters, what is its surface area?

• 123.45 square meters

• 314.16 square meters

• 615.44 square meters

• 456.78 square meters

For a sphere with a radius of 11 inches, what is the calculated surface area?

• 1000.00 square inches

• 1210.56 square inches

• 1519.76 square inches

• 2000.00 square inches