GCSE Secondary Maths Age 13-17 - Geometry & Measures: Similar Shapes - Explained

The video tutorial explains how to solve a problem involving scale factors and volume ratios. It begins by introducing the concept of scale factors and the problem setup, which involves two shapes with given surface area and volume ratios. The tutorial then explains how to derive the linear and volume ratios from the area ratio. It provides a step-by-step solution to find the volume of one shape using the given data and scale factors. The video also includes a marking scheme and tips for students to achieve full marks, emphasizing the importance of understanding the relationship between linear, area, and volume ratios.

What is the initial ratio of the surface areas of shapes A and B?

• 2:3

• 3:4

• 4:5

• 5:6

How do you find the linear ratio from the area ratio?

• Square root the area ratio

• Cube the area ratio

• Multiply the area ratio by 2

• Square the area ratio

What is the next step after finding the linear ratio to determine the volume ratio?

• Add the linear ratio

• Cube the linear ratio

• Subtract the linear ratio

• Divide the linear ratio by 2

What is the volume of shape B given in the problem?

• 12 cm³

• 8 cm³

• 5 cm³

• 10 cm³

How do you calculate the volume of shape A?

• Divide the volume of B by the scale factor

• Add the volume of B to the scale factor

• Multiply the volume of B by the scale factor

• Subtract the scale factor from the volume of B

What is the final volume of shape A rounded to three significant figures?

• 6.52

• 6.49

• 6.50

• 6.51

What is the key concept to remember when solving these types of problems?

• The connection between lengths, areas, and volumes

• The exact measurements of shape B

• The difference between shapes A and B

• The color of the shapes