Respuesta :
Answer:
C. The volume is 1/8 the original volume
Explanation:
Step 1. To find how the volume changes if the diameter is reduced to one-half of the original size, we will test two scenarios:
• In the first scenario, the diameter will be 2, and in the second scenario, the diameter will be one-half of 2 which is 1.
We will find the volume for these two cases and see how it changes.
Step 2. For a diameter of d=2.
If the diameter is 2, the radius is:
[tex]\begin{gathered} r=d/2 \\ r=2/2 \\ r=1 \end{gathered}[/tex]Using the volume formula for a sphere:
[tex]V=\frac{4\pi}{3}r^3[/tex]In this case:
[tex]V=\frac{4\pi}{3}(1)^3[/tex]We will call this volume, V1:
[tex]V_1=\frac{4\pi}{3}[/tex]Step 3. Now we will find the volume for the second case in which the diameter is d=1.
The radius is:
[tex]\begin{gathered} r=d/2 \\ r=1/2 \\ \end{gathered}[/tex]Using the same formula for the volume:
[tex]V=\frac{4\pi}{3}(\frac{1}{2})^3[/tex]Solving the operations:
[tex]V=\frac{4\pi}{3}(\frac{1}{8})^[/tex]We will call this V2:
[tex]V_2=\frac{4\pi}{3}(\frac{1}{8})^[/tex]Step 4. As you can see, the first part of the previous expression is V1:
[tex]\begin{gathered} V_{1}=\frac{4\pi}{3} \\ V_2=\frac{4\pi}{3}(\frac{1}{8}) \end{gathered}[/tex]Therefore:
[tex]V_2=V_1(\frac{1}{8})[/tex]The second volume is the first volume multiplyed by 1/8 ⇒ it is 1/8 of the original volume.
Answer:
C. The volume is 1/8 the original volume
