Question

!!!HELP!!! PLEASE SHOW WORK SO I CAN UNDERSTAND!

Answer 1

The only part of this problem that's the least bit tricky is knowing
the formula for the volume of a sphere.  Here is is:

          Volume of a sphere = (4/3) (pi) (radius of the sphere)³  .

Everything else is just arithmetic.

pi . . . use 3.14
Radius . . . 2-1/8 inches.  It'll be easier if we write that as  2.125 inches.

Now, just put the numbers into their places in the formula:

         Volume = (4/3) (pi) (radius of the sphere)³

                     = (4/3) (3.14) (2.125)³

and run that through your calculator.

When I run it through mine, I get  40.174 in³ .

None of the choices is anywhere near that number.
I'm worried, and I don't understand that.

Maybe we should look back at the question, and notice that
it says "estimate" ... something you do quickly in your head.

OK.  We know the real formula ...   Volume = (4/3) (pi) (radius)³ .
How could we estimate this quickly in our head?

pi . . . instead of 3.14, just use 3

radius . . . instead of 2-1/8, just use 2 .  Then (radius)³ = 2 x 2 x 2 = 8

Then  (4/3) (pi) (radius)³ = (4/3) (3) (8) = (4/3) of 24  =  32 .

Well now, will you look at that !  I guess that's where the 32 came from
on the list of choices.