Exploring Volume and Surface Area of Spheres

The video tutorial covers the geometry of spheres, focusing on calculating volume and surface area. It begins with an introduction to the basic components of a sphere, such as the diameter, radius, and great circle. The tutorial then explains how to calculate the volume of a sphere using the formula 4/3 πr³, and how to find the surface area using 4πr². Real-world applications are discussed, including how to determine the amount of material needed to fill or cover a sphere. The video concludes with practical exercises to reinforce the concepts learned.

What is the formula to calculate the volume of a sphere?

• 2 * pi * radius^2

• 4/3 * pi * radius^3

• 4 * pi * radius^2

• pi * radius^2

If the diameter of a sphere is 10 units, what is its radius?

• 10 units

• 15 units

• 20 units

• 5 units

How do you calculate the surface area of a sphere?

• radius^2 / pi

• 2 * pi * radius

• 4 * pi * radius^2

• pi * radius^2

What is the surface area of a sphere with a radius of 3 units?

• 36 * pi units^2

• 12 * pi units^2

• 9 * pi units^2

• 27 * pi units^2

If the surface area of a sphere is 314.16 square units, what is the radius?

• 5 units

• 10 units

• 3 units

• 7 units

How do you find the diameter of a sphere if you know the surface area?

• Divide the surface area by pi

• Multiply the surface area by 4

• Square root the surface area and multiply by 2

• Calculate the radius from the surface area and double it

In a box filled with 4 spheres and cotton, if each sphere has a radius of 2.5 inches, what is the diameter of each sphere?

• 7.5 inches

• 10 inches

• 2.5 inches

• 5 inches

How do you calculate the total volume of cotton needed to fill the remaining space in the box?

• Subtract the volume of all spheres from the box volume

• Add the volume of all spheres to the box volume

• Multiply the volume of one sphere by four

• Divide the box volume by the volume of one sphere

What is the first step in finding the surface area of a basketball if you only know the circumference?

• Square the circumference

• Find the radius using the circumference

• Multiply the circumference by pi

• Divide the circumference by 4

If you need help understanding the calculations, what should you do?

• Contact the teacher for guidance

• Guess the answers

• Wait for the answers to be revealed

• Skip the questions