Imagine a sphere. If the sphere is cut three times at right angles, the resulting pieces would be what fraction of the original sphere?

Question

 this question is about the chapter 12 of general chemistry II.  I took this class in college in Dallas. It is about sphere.

 

I also want to know how to draw 1/4 sphere

 

I would highly appreciate your help, thanks

I have been stuck with this question quite a while :((

Answer 1

Hi Suzy.

 

If you cut a sphere in half each piece is 1/2 of the original sphere

If you cut the halves in half, each piece is 1/4 of the original sphere

If you cut those quarters in half, each pice is 1/8 of the original sphere

 

If you think of this in terms of geography, imagine cutting a globe along the longitudinal lines of the prime meridian and international date line as your first cut.

For your second cut, cut along the longitudinal lines of 90 degrees east and 90 degrees west.

The third cut would be at the equator.

Each of these cuts is at right angles to the previous cut.

 

To draw a 1/4 sphere, try starting with 1/4 circle and make it 3-dimensional

Or imagine a one sector of a 3-dimensional (x,y,z) axis.

Answer 2

Think of a globe. Slice it from the top. You now have two half spheres.

Rotate you knife 90°. Slice it again from the top. You now have four quarters.

Take the knife and slice through the "equator." You now have 8 pieces.