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The formula for the volume of a sphere, V, in terms of its radius, r, is:
V = 4/3 πr3
We can rearrange this formula to make r the subject.
If we multiply both sides by 3, we reach:
3V = 4πr3
Then we can divide both sides by 4π to reach:
r3 = 3V / 4π
Finally, we need to find the cubed root of both sides and the formula for the radius of a sphere, r, in terms of its volume, V, is:
Example
Calculate the radius, r cm, of a sphere which has a volume of 100 cm3.
Give your answer to 3 significant figures.
V = 4/3 πr3
100 = 4/3 πr3
Multiply both sides by 3: 300 = 4πr3
Divide both sides by 4π: 300 / 4π = r3
Find the cube root of this total: r = 3√ 300 / 4π
r = 3√23.873... = 2.8794... ≈ 2.88 cm (to 3 s.f.)
It looks complicated, but just take it one step at a time.
Let's give it a go!
Question
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