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

the answer is option C