A sphere is dilated by a scale factor of 1.04 to create a new sphere. How does the volume of the new sphere compare with the volume of the original sphere?

It's not clear what you mean by "dilated". That's not really a mathematical operation ... at least not on the level of math that we're operating on here.
I'm going to assume that you mean that the linear dimension of the sphere is increased by a factor of 1.04 . A sphere actually has only one linear dimension ... its diameter, or what is equivalent, its radius.
The volume of a sphere is V = (4/3) (pi) (radius)³ so we can see that the volume changes as the cube of the radius.
If the radius increases by a factor of 1.04, then the volume also increases, but by a factor of
(1.04) x (1.04) x (1.04) = 1.124864
This is very interesting. By increasing the diameter of the sphere only 4 percent, you increased its volume by almost 12 and 1/2 percent.

Answered by AL2006 | 2024-06-10

When a sphere is dilated by a scale factor of 1.04, its volume increases by approximately 12.49%. This is because the volume scales with the cube of the radius. Thus, the new volume is about 1.124864 times the original volume.
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Answered by AL2006 | 2024-12-26