<u>First Part</u>
Given that
We have that
<u>Second Part</u>
Given that
If the Diameter were reduced by half we have that
This shows that the volume would be of its original volume
<u>First Part</u>
Gather Information
Calculate Radius from Diameter
Use the Radius on the Volume formula
Before starting any calculation, we try to simplify everything we can by expanding the exponent and then factoring one of the 9s
We can see now that one of the 3s can be already divided by the 3 in the denominator
Finally, since we can't simplify anymore we just calculate it's volume
<u>Second Part</u>
Understanding how the Diameter reduced by half would change the Radius
Understanding how the Radius now changes the Volume
With the original Diameter, we have that
If the Diameter were reduced by half, we have that
But we can see that the numerator is exactly the original Volume!
This shows us that the Volume would be of the original Volume if the Diameter were reduced by half.