Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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?

Sagot :

AL2006
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.
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.