Knowing that the cones are similar, the volumes of the cones will be = 4
3 : r
3.
We also know that the volume of the larger cone will be 3x the volume of the smaller one, so 3b: b, where b is the volume of the smaller cone, which is r
3. Thus we actually have:
Spoiler
r3 = b
The question states that the larger cone's volume is 3 times that of the smaller cone's.
If I call the smaller cone's volume 'b', then 3b is the larger cone's volume.
We found that smaller cone's volume (b) is also r3 when scaled from length.
Substitute b = r3 into 3b and you get: 3b = 3r3.
3b = 3r3 = 43 = 64
This can help you find r, which would be:
Spoiler
3r3 = 64
r3 = 64/3
r = cube root of 64/3 = 2.77 cm approx.
which rounds to 2.8.
This gives Option E.