Volume of spherical water feature

Difficulty:
higher

Rating:
4-stars

GCSE Marks:
4-marks

GCSE Text:
Neil has a spherical water feature, which he would like to upgrade to a similar but larger model. To do this, he needs key information to compare products online. Neil measures the circumference around the centre of the existing water feature as 150cm.

shere-1

a) Rearrange the given formula to make D (the diameter) the subject, and calculate the diameter of Neil’s existing water feature.

You are given that the volume of any sphere can be found using:

sphere-2

b) Calculate the volume (in cm³) of Neil’s existing water feature (2 s.f.)

Suggestions:
All but the most able students are normally horrified when seeing this question, therefore a good skill to emphasise is the ability to break a large problem into smaller manageable steps.  This video seems to work best when staff let students struggle a little, as it requires them to reverse a normal operation for the first part at least. It also tests the core skill to find the radius when given a diameter and vice versa.

Extension Ideas:
Teachers could extend the learning by considering:

  • Convert your answer to m³
  • If Neil wants a new water feature with a diameter that is 20% bigger, what will be the volume of that enlarged sphere?
  • Neil sees a similar water feature on sale with a volume quoted at 0.5m³. How much bigger is the diameter of this water feature compared to his existing one?

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