Question

Cone A has a radius 12 inches and Cone B has a radius of 30 inches. If the cones are similar and the volume of Cone A if 48, find the volume of Cone B.

Answer 1

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.

_____

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

Answer 2

Answer:

750 cubic inches.....