### Video Transcript

The formula to calculate the volume
of a sphere is π equals four-thirds ππ cubed. Make π the subject. Thereβs also a second part to this
question. Find the radius of a sphere with a
volume of 900 cubic centimeters. Give your answer accurate to two
decimal places.

Well, when weβre trying to change
the subject to a formula, what we need to do is carry out inverse operations. But before we do that, what Iβm
going to do is rewrite our formula in a way that will make the next stage
easier. And we can rewrite it like
this. π is equal to four ππ cubed over
three.

And if you think about why we can
do that and why can we rewrite in this way. If weβre multiplying four-thirds by
and then weβve got π over one, cause weβre gonna turn them all into fractions, then
multiply it by π cubed over one, then what this would mean is weβd multiply the
numerators, say four ππ cubed. And then weβd multiply the
denominators, three by one by one which would give us three. So, thatβs how we got our four ππ
cubed over three.

So, now we can carry out our
inverse operations. The first of which is to multiply
each side of the equation by three. And when weβve done that, weβll
have three π is equal to four ππ cubed. So, now weβre gonna divide each
side of the formula by four π. And weβre gonna do that because we
want to make π the subject, so we want π on its own. And if we divide four ππ cubed by
four π, weβre gonna be left with π cubed. And we need to remember that
whatever we do to one side of the formula, we must do to the other.

So, now weβve got three π over
four π is equal to π cubed. So, great, have we finished because
π is on its own? Well, no, because we want to make
π the subject of the formula, not π cubed. So, we need to carry out one more
step. And this final step is to complete
the inverse operation of cubing π, and that is to take the cube root. So, weβre gonna take the cube root
of both sides of our formula. And when we do that, weβre gonna
get the cube root of three π over four π is equal to π.

So therefore, we can say that if we
make π the subject to the formula, and the formula is π equals four thirds ππ
cubed, then π is equal to the cube root of three π over four π.

So, now for the second part of this
question, weβre asked to find the radius of a sphere when weβve been given the
volume. And that volume is 900 cubic
centimeters. Well, we can use the formula that
we found in part one. And thatβs because π is now the
subject. So, now we can also write down our
other information. And that is that the volume is
equal to 900. And we can substitute this into our
formula to find π, the radius.

So, we put 900 into our
formula. Weβre gonna get π is equal to the
cube root of three multiplied by 900 over four π. And this can be rewritten as π is
equal to the cube root of 2700 over four π. Thatβs because three multiplied by
900 is 2700 cause three multiplied by nine is 27, then we have two zeros.

Now itβs worth reminding ourselves
that we could put this into calculator as it is. Or we could use this rule to help
us put it into the calculator in another way. So, we know that the cube root of
π over π is the same as the cube root of π divided by the cube root of π. So, you could either put the whole
sort of the expression into your calculator as we have it, or you could put the cube
root of 2700 divided by the cube root of four π.

So, when we work this out by
calculator, we get π is equal to 5.989418137. But we havenβt finished there. And thatβs because the question
asked us to give our answer accurate to two decimal places. So therefore, we count down two
decimal places. And that gives us our eight. So, Iβve drawn a line after
that. Then our deciding number is the
nine, which is the digit to the right of our eight. And as thatβs five or higher, it
means that weβre gonna round our eight up. So, itβs gonna round up to a
nine. So therefore, we can say that the
radius of a sphere with a volume of 900 cubic centimeters is going to be 5.99
centimeters, and thatβs to two decimal places.