3D Shapes - Volume

The video tutorial explains how to find the height of a frustum from a large cone using volume ratios. It begins by establishing the relationship between the large cone, the small cone, and the frustum. The tutorial then demonstrates how to use cube roots to find the ratio of lengths and derive an expression for the frustum's height in terms of the large cone's height. The video also discusses the marking scheme and highlights the importance of understanding relationships over using formulas due to limited information.

What are the three parts of the cone mentioned in the problem?

• Frustum, cylinder, and small cone

• Large cone, cylinder, and small cone

• Large cone, frustum, and small cone

• Large cone, frustum, and cylinder

What is the volume ratio of the small cone to the large cone?

• 98:27

• 125:27

• 98:125

• 27:125

What is the cube root of the volume ratio 27:125?

• 25:9

• 9:25

• 3:5

• 5:3

What fraction represents the height of the frustum in terms of the large cone's height?

• 2/5

• 4/5

• 1/5

• 3/5

How many marks are available for identifying the cube numbers in the ratio?

• Three marks

• One mark

• Four marks

• Two marks

What is the final expression for the height of the frustum in terms of H?

• 3/5 H

• 5/2 H

• 2/5 H

• H/5

Why can't the formula for the volume of the cone be used directly to find the height?

• The height is already known

• Insufficient information about the radius and height

• The volume is not given

• The formula is incorrect