Upper bound volume

Difficulty:
higher
Rating:
5-stars
GCSE Marks:
5-marks

GCSE Text:
The design of a ‘donut’ shaped pond is shown below. You are given the radius of the outside of the pond, the radius of the island inside the pond and the depth of the water. Each of the given measurements has been rounded to 2 sig. fig.

bound of pond volume

Calculate the upper bound for the volume of water in the pond, giving your answer in m³ and rounded to 4 sig. fig.

Suggestions:
This question works well to consolidate learning of complex bounds. Whilst the question needs quite  bit of thought to get all marks, students often see this as a question where easy marks can be gained by completing basic steps.  Students take 3-4 minutes to answer this question in full, and the extension question works well to stretch students who finish early.

Teachers could extend the learning by considering:

  • The gardener wants to replace the water pump that filters the water, but the specifications are in cm³.  State the upper bound of the pond volume in cm³.
  • State the error interval for the volume of water in the pond.

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