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

Fred is creating two rectangular flower beds, with the larger being three times the size of the smaller. The video explains how to calculate the soil needed for the larger bed using the ratio of dimensions and areas. The key concept is that if the dimensions are in a 3:1 ratio, the areas are in a 9:1 ratio. Therefore, the larger bed requires nine times the soil of the smaller one, totaling 1620 kilograms. The video also highlights the importance of understanding ratios for dimensions, areas, and volumes.

What is the relationship between the dimensions of the larger and smaller flower beds?

• The larger bed is twice the size of the smaller bed.

• The larger bed is the same size as the smaller bed.

• The larger bed is three times the size of the smaller bed.

• The larger bed is four times the size of the smaller bed.

How much soil is needed for the larger flower bed if the smaller one requires 180 kilograms?

• 540 kilograms

• 720 kilograms

• 1620 kilograms

• 1800 kilograms

If the dimensions of two rectangles are in a 3:1 ratio, what is the ratio of their areas?

• 3:1

• 6:1

• 9:1

• 12:1

What is the ratio of volumes if the dimensions are in a 1:3 ratio?

• 1:9

• 1:27

• 1:3

• 1:6

Which of the following statements is true about the relationship between dimensions and areas?

• If dimensions are in a 1:3 ratio, areas are in a 1:12 ratio.

• If dimensions are in a 1:3 ratio, areas are in a 1:9 ratio.

• If dimensions are in a 1:3 ratio, areas are in a 1:3 ratio.

• If dimensions are in a 1:3 ratio, areas are in a 1:6 ratio.