Volume of gravel path

Difficulty:
intermediate

Rating:
4-stars
GCSE Marks:
4-marks

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

gravel-path

a) Calculate the volume of gravel she needs to create this path.

Gravel is delivered in sacks with the following dimension:
gravel-2

b) How many sacks of gravel will need to be ordered to finish 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:

  • 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 (2dp)?

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