GCSE Secondary Maths Age 13-17 - Geometry & Measures: Ratio of Volumes - Explained

The video tutorial explains how to determine the volume of solid A given the volume of solid B and the ratio of their surface areas. It covers the concept of mathematically similar shapes, focusing on the relationship between surface area, linear, and volume ratios. The tutorial provides a step-by-step calculation to find the volume of solid A, emphasizing the importance of understanding and applying these ratios correctly.

What is the given ratio of the surface areas of solids A and B?

• 4 to 9

• 3 to 5

• 6 to 8

• 5 to 7

How do you find the ratio of linear measurements from the ratio of surface areas?

• By halving the surface area ratio

• By doubling the surface area ratio

• By taking the square root of the surface area ratio

• By cubing the surface area ratio

What is the ratio of the volumes of solids A and B?

• 4 to 9

• 16 to 81

• 2 to 3

• 8 to 27

If the volume of solid B is 405 cm³, what is the volume of solid A?

• 135 cm³

• 90 cm³

• 150 cm³

• 120 cm³

What is the key step in solving the problem of finding the volume of solid A?

• Finding the ratio of surface areas

• Multiplying the volume ratio by the factor used for solid B

• Calculating the square of the linear ratio

• Understanding the relationship between linear, area, and volume ratios