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Current time:0:00Total duration:3:29

- [Instructor] The volume
of right circular cone A is four cubic meters. What is the volume in cubic
meters of a right circular cone with 2.5 times the radius and seven times the height of cone A. Pause this video and think
about this on your own before we work through this together. All right. So let's think about the volume of cone A. Well, we know it's four cubic meters. We also know what the formula for this is. It's going to be 1/3 times pi times the radius of the
circular base squared times the height and that's going to be, of
course, four cubic meters, so that's what they told us. Now, let's think about
the volume of this new, large cone, larger cone. What's it going to be? Well, it's going to be 1/3 times pi. Now what's the radius going
to be for this larger one? Well, it says that it
is 2.5 times the radius, so if r is the radius
of our original cone, now we're going to have 2.5r squared. That's the radius of this larger cone, the radius of its base of the larger cone and then what's its height? Well, instead of a height of just h, we're now going to have a
height of seven times h, so let me write this times seven h and now what is this going to give us? Well, let's see. This is going to be equal to 1/3 pi times 2.5 squared is 6.25. So it's going to be 6.25r
squared times 7h times 7h and now what I'm going to do is I'm gonna take out all of
the parts of this expression that essentially make up the volume of A and then see what we're scaling it by. So if we take, we have
a 1/3 pi r squared h, so 1/3 pi r squared h. So this is equal to 1/3 pi r squared h times, what do we have leftover? We have 6.25 times seven. So times 6.25 times seven. Now we know what I have here in black. This is the volume of our original cone, which they told us is four cubic meters. So this is equal to four right over here and so let's see what's four times 6.25? That's going to be 24 plus one, so it's 25 times seven is going to be
equal to 175 cubic meters, which is exactly what we
have here for choice C. Now another way that you
could have thought about this is saying, all right, my
volume is based on the square of the radius and the height, so if I increase my radius by 2.5 times, that's gonna increase my volume by the square of that by 6.25 times and if I increase my height
by a factor of seven, well, I just have an h there, not an h squared, so that's going to increase my
volume by a factor of seven. So overall, we're going
to increase our volume by a factor of seven times 6.25 and then you multiply that
times the four cubic meters and you once again get
to the 175 meters cubed.