Geometry and Volume Calculations

This video tutorial covers Math 8 Unit 5 Lesson 19, focusing on estimating the volume of a hemisphere. The teacher explains the concept of a hemisphere and demonstrates how to estimate its volume using a cube and a cone. The lesson also includes calculating the height of a cone and the diameter of a cylinder based on given volumes. The tutorial concludes with solving linear equations, providing a comprehensive understanding of these mathematical concepts.

What is a hemisphere?

• Half of a sphere

• A quarter of a sphere

• A full sphere

• A flat circle

If a hemisphere fits inside a cube with a base edge of 10 inches, what is the approximate volume of the cube?

• 100 cubic inches

• 1000 cubic inches

• 200 cubic inches

• 500 cubic inches

What fraction of a sphere's volume is a hemisphere's volume approximately?

• 1/4

• 1/2

• 2/3

• 3/4

Given a cone with a volume of 16.5 cubic inches, what is the formula used to find its height?

• Volume = 1/3 π r² h

• Volume = 1/2 π r² h

• Volume = π r² h

• Volume = 2/3 π r² h

If the radius of a cone is 1.5 inches, what is the height when the volume is 16.5 cubic inches?

• 4 inches

• 6 inches

• 3 inches

• 5 inches

What is the first step in determining the diameter of a cylinder given its volume?

• Multiply the volume by π

• Divide the volume by the height

• Subtract the height from the volume

• Multiply the volume by the height

After correcting a calculation mistake, what is the diameter of the cylinder?

• 12

• 16

• 18

• 14

In solving the equation 7 = 6 - 3, what is the first step?

• Add 3 to both sides

• Subtract 3 from both sides

• Divide both sides by 2

• Multiply both sides by 2

What is the value of M in the equation 4 = -2M?

• 1

• -2

• 2

• -1

What is the final step in solving the equation 4 = -2M?

• Multiply both sides by -2

• Divide both sides by -2

• Add 2 to both sides

• Subtract 2 from both sides