Finding the Radius of a Sphere from Surface Area

The video tutorial explains how to find the radius of a sphere when given its surface area. It begins by introducing the problem and the surface area formula, 4πr². The instructor then sets up the equation by substituting the given surface area value, 256π, into the formula. The tutorial proceeds to solve the equation by canceling π, dividing by 4, and taking the square root to find the radius. The instructor emphasizes the importance of considering only the positive value for the radius, as it represents a physical measurement. The video concludes with the final answer, noting the absence of specific units.

What is the initial problem discussed in the video?

• Finding the volume of a sphere

• Finding the radius of a sphere given its surface area

• Finding the diameter of a sphere

• Finding the circumference of a sphere

What formula is used to find the surface area of a sphere?

• 4/3 pi r cubed

• pi r squared

• 4 pi r squared

• 2 pi r

What value is substituted for the surface area in the formula?

• 256 pi

• 64 pi

• 512 pi

• 128 pi

What is the first step in simplifying the equation 256 pi = 4 pi r squared?

• Divide both sides by pi

• Add pi to both sides

• Multiply both sides by pi

• Subtract pi from both sides

After canceling pi, what is the simplified equation?

• 256 = 4 r

• 256 = r squared

• 256 = 2 r squared

• 256 = 4 r squared

What operation is performed after dividing 256 by 4?

• Add 4 to both sides

• Multiply both sides by 4

• Take the square root of both sides

• Square both sides

What is the value of the radius after solving the equation?

• 8

• 4

• 12

• 16

Why is only the positive value of the radius considered?

• The radius cannot be negative

• Negative values are not allowed in algebra

• Negative values are not real numbers

• The formula only works with positive values

What is the unit of the radius in the final answer?

• Cubic units

• Units squared

• Units

• No unit