Applying maths to solve problems in the real world…

Volume of spherical water feature

Difficulty: Rating:

GCSE 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.

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:

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?