Question

3. The diameter of a spherical balloon shrinks to one-half of its original size. How does this affect the volume? Hint: Test two scenarios and compare the volumes! Show your work!!“Use 3.14 for Pi”A. The volume is cut in halfB. The volume doublesC. The volume is 1/8 the original volumeD. The volume is 1/4 the original volume

Answer 1

Remember that

The volume of a sphere is equal to

$V=\frac{4}{3}*pi*r^3$

we have that

the diameter is reduced to half its original size

D=D/2

so

the new radius is

r=r/2

substitute in the formula of volume

$V=\frac{4}{3}*p\imaginaryI *(\frac{r}{2})^3$$\begin{gathered} V=\frac{4}{3}*p\imaginaryI *\frac{r^3}{2^3} \\ V=\frac{1}{8}*\frac{4}{3}*p\imaginaryI *r^3 \end{gathered}$

the answer is option C