Volume and Radius of a Sphere

The video tutorial explains how to calculate the volume of a sphere when the radius is given. It introduces a formula where the radius is expressed as a function of volume, which is less common. The tutorial walks through the steps of solving for volume by cubing both sides of the equation to eliminate the cube root, simplifying the equation, and performing arithmetic operations to find the final volume in cubic inches. The process includes checking divisibility and performing multiplication to arrive at the final result of 288π cubic inches.

What is the formula used to calculate the radius of a sphere from its volume?

• r = cube root of (3v/4π)

• r = v/3π

• r = 4π/3v

• r = 3v/4π

In the given problem, what is the radius of the sphere?

• 6 inches

• 7 inches

• 4 inches

• 5 inches

What is the first step to solve for the volume when given the radius?

• Divide both sides by 3

• Take the square root of both sides

• Cube both sides of the equation

• Multiply both sides by 4π

After cubing both sides, what does the left-hand side of the equation become?

• 36 cubic inches

• 216 cubic inches

• 72 cubic inches

• 144 cubic inches

What operation is performed to isolate the volume on one side of the equation?

• Multiply by the inverse of the coefficient

• Divide by 216

• Add 4π to both sides

• Subtract 3 from both sides

How do you determine if 216 is divisible by 3?

• Check if the last digit is 3

• Multiply the digits together

• Add the digits and see if the sum is divisible by 3

• Subtract 3 from the number

What is the result of dividing 216 by 3?

• 76

• 68

• 72

• 74

What is the final volume of the sphere in terms of π?

• 144π cubic inches

• 216π cubic inches

• 72π cubic inches

• 288π cubic inches

What is the purpose of multiplying by 4π/3 in the equation?

• To cancel out the cube root

• To convert inches to cubic inches

• To cancel out the 3/4π

• To simplify the equation

What is the significance of the final answer being in cubic inches?

• It represents the surface area

• It represents the diameter

• It represents the volume

• It represents the circumference