Answer:
750 cubic inches
Step-by-step explanation:
The ratio of linear dimensions is ...
(radius B)/(radius A) = (30 in)/(12 in) = 2.5
Then the ratio of volumes is
(volume B)/(volume A) = (2.5)^3 = 15.625
So, ...
volume B = (volume A)·15.625 = 750 . . . . cubic inches
The volume of Cone B is 750 cubic inches.
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The ratio of volumes is the cube of the ratio of linear dimensions (radius) when the figures are similar.
If the volume of Cone A is ...
V = (π/3)r^2h
and the ratio of dimensions is k, then the volume of Cone B is ...
V = (π/3)(kr)^2(kh) = (π/3)r^2h(k^3) . . . . k^3 times the volume of Cone A
