# Algebra

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The volume of a sphere is given by:

V=4/3 pie r cubed.

Use the formula, and show your workings, to find out what happens to the volume of a sphere if r is halved and r is trippled?

Please help as this has just completly lost me, i end up with

V = 4/3 Pie r cubed / eight .....for half of r.

• Algebra -

You were correct,
when you cut the radius in half, the volume will be 1/8 of the original.

When you triple the radius, the new volume will be 27 times that of the original.

Look at what happens when we substitute the new radius for r

sub in 3r for the radius
V = (4/3)π(3r)^3
= (4/3)π)(27)r^3
= 27 * (4/3)πr^3

Notice that the volume changes by the cube of the scaling factor,
taking 1/2 ----> (1/2)^3 = 1/8

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