Applying maths to solve problems in the real world…

Area & volume of gravel path

Difficulty: Rating:

GCSE Marks:

GCSE Text: Heather wants to create a gravel path made from two rectangles and a triangle with the following dimensions:

a) Calculate the area of black weed control membrane that she needs to use to cover the exact area of the path.

The depth of the gravel to be put on top of the membrane is 8cm.

b) Calculate the volume of gravel needed to create the path.

Suggestions:
This is a good GCSE level question for the foundation or higher papers. It requires students to recall the formulae for the area of triangles and rectangles, and to carefully select the right dimensions. Common mistakes are that students multiply the area by 8 in step 2, rather than converting all units to metres. Some students break up the volume questions into 3 distinct shapes, so it is useful to highlight the quick way of multiplying the cross sectional area by the depth in one step to avoid possible errors.

Extension Ideas: Teachers could extend the learning by considering:

If weed membrane comes on rolls of 8m² and gravel is delivered in sacks of 1m³, how many rolls of membrane and how many sacks of gravel are needed to create this path?

Rather than waste gravel, any surplus is spread on top of the path, increasing the depth of gravel. What will the new depth of gravel be if it is evenly spread?