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.

  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

750 cubic inches

step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15

step by step solution :

step   1   :

1.1     4 = 22

(4)3 = (22)3 = 26

equation at the end of step   1   :

  ((23) • 26)2

step   2   :

equation at the end of step   2   :

  (23 • 26)2

step   3   :

final result :

  218

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