SOLUTION:
Case: Volume of Sphere
Method:
a) The volume of a sphere whose diameter, d= 28in
The radius,
r= 28/2
r= 14 in
The Volume, therefore:
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ V=\frac{4}{3}\pi\times14\times14\times14 \\ V=11494.04\text{ }cubic\text{ }inches \end{gathered}[/tex]
b) When half of the volume is used,
[tex]\begin{gathered} V=\frac{1}{2}V_0 \\ V=\frac{1}{2}\times11494.04 \\ V=5747.02\text{ }cubic\text{ }inches \end{gathered}[/tex]
c) The radius of the halved volume
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ 5747.02=\frac{4}{3}\pi r^3 \\ r^3=\frac{3\times5747.02}{4\pi} \\ r^3=1372 \\ r=\sqrt[3]{1372} \\ r=11.11\text{ }inches \end{gathered}[/tex]
Final answer: (To 2 d.p)
a) 11494.04 cubic inches
b) 5747.02 cubic inches
c) 11.11 inches
