Video Transcript
Cones A and B are similar. Calculate the volume of cone B.
So if you look at the information
in the question, you’ll see that we’re given a length for cone A and a length for
cone B. They’re both the radius of the
circle on the base. And we’re also told the volume of
cone A. And we need to use all of this
information together to calculate the volume of cone B. So to start off this question then,
we’re given corresponding lengths in the two cones, which means we can write down
the ratio of the lengths. So the length ratio between the two
cones is three to six, but of course that will simplify to one to two by dividing
both sides by three. From this we can then calculate the
volume ratio, because remember we saw that, in order to calculate the volume ratio
from the length ratio, we need to cube both parts of it. So the volume ratio is one cubed to
two cubed, which of course is just one to eight.
What this means then is that the
volume of cone B is eight times larger than the volume of cone A. So I can calculate it by taking the
volume of cone A, which is 70 centimetres cubed, and multiplying it by eight. And doing so, it gives me an answer
then of 560 cubic centimetres for the volume of cone B. So the important thing to note in
this question is it we didn’t have to use a formula for calculating the volume of a
cone, even though of course such formula does exist. We just used the relationship
between the volumes of the two cone due to the similarity of them.
