Exploring the Volume of a Sphere

This video tutorial covers the concept of spheres, focusing on their volume calculation. It begins with an introduction to spheres and their properties, followed by the formula for calculating the volume of a sphere. The tutorial includes example calculations, demonstrating how to apply the formula. It also explains the concept of perfect cubes and cube roots, which are essential for understanding the calculations. Finally, the video shows how to find the radius of a sphere when given its volume.

What defines a sphere?

• A 2D shape with varying distances from the center

• A 3D shape with varying distances from the center

• A 3D shape with all points at equal distances from the center

• A 2D shape with all points at equal distances from the center

What is the formula for the volume of a sphere?

• V = πr³

• V = 4/3 πr³

• V = πr²

• V = 2/3 πr³

How do you calculate the volume of a sphere?

• Use the diameter in the formula V = 4/3 πd³

• Use the radius in the formula V = 4/3 πr³

• Use the circumference in the formula V = 1/3 πc³

• Use the area in the formula V = πa³

How do you calculate the volume of a sphere with a radius of 4 cm?

• 523.6 cm³

• 33.5 cm³

• 268.1 cm³

• 150.8 cm³

If a sphere's diameter is 10 feet, what is its radius?

• 10 feet

• 20 feet

• 5 feet

• 2.5 feet

What is the volume of a sphere with a radius of 5 feet?

• 125 feet³

• 65.4 feet³

• 523.6 feet³

• 314.2 feet³

What is a perfect cube?

• A number that can be cubed to get another whole number

• A number that can be cubed to get a whole number

• A number that can be squared to get a whole number

• A number that can be divided by 3 to get a whole number

What is the cube root of 64?

• 4

• 8

• 3

• 16

Given a volume of 288π inches³, what is the radius of the sphere?

• 6 inches

• 12 inches

• 18 inches

• 3 inches

How do you find the radius from the volume of a sphere?

• Take the square root of the volume divided by π

• Square the volume and divide by π

• Divide the volume by 4/3π and take the cube root

• Multiply the volume by 3/4π