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, fin

Question

3 years ago

11

d the volume of Cone B.

2 answers:

ziro4ka [17] · Answer 1 · 2022-03-18T23:58:25+03:00

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

Ilia_Sergeevich [38] · Answer 2 · 2022-03-19T01:56:43+03:00

4 0

Answer:

750 cubic inches.....