Volume and Surface Area Concepts

This video tutorial covers Math 8 Unit 5 Lesson 21, focusing on cylinders, cones, and spheres. It begins with an introduction to the lesson's topics, followed by a task to order spheres by volume. The tutorial then demonstrates how to calculate the volume of a cone using a given formula and approximations. Next, it explains how to find the volume of a cylinder with the same dimensions as the cone. Finally, the video concludes with solving linear equations, providing step-by-step guidance for each problem.

What is the first step in ordering spheres by volume?

• Determine the radius of each sphere.

• List the spheres in alphabetical order.

• Sketch each sphere to visualize their sizes.

• Calculate the surface area of each sphere.

If a sphere has a radius of 4, what is its diameter?

• 4

• 16

• 8

• 2

What is the formula used to calculate the volume of a cone?

• 1/3πr²h

• 2πr²h

• πr²

• πr²h

What is the approximate value of Pi used in the cone volume calculation?

• 3.50

• 3.14

• 3.75

• 3.00

How do you find the height of a cone if the volume and radius are known?

• Multiply the volume by the radius.

• Divide the volume by the radius.

• Divide the volume by the radius squared and Pi.

• Multiply the volume by Pi and the radius squared.

What is the formula for the volume of a cylinder?

• πr²h

• πr²

• 1/3πr²h

• 2πr²h

How does the volume of a cylinder compare to that of a cone with the same dimensions?

• The cylinder has less volume.

• The cylinder has more volume.

• The volumes cannot be compared.

• The cylinder has the same volume.

What is the solution to the equation 8x - 7 = 4?

• x = 1

• x = 2

• x = 3

• x = 4

How do you eliminate a fraction in an equation like 1/3x = 10?

• Multiply both sides by 3.

• Add 3 to both sides.

• Subtract 3 from both sides.

• Divide both sides by 3.

What is the value of x in the equation 1/3x = 10?

• x = 20

• x = 30

• x = 40

• x = 10