Answer:
r=14 cm
V=11499 cubic cm
Step-by-step explanation:
If the radius of the sphere is r cm, then the perimeter of the largest cross section is the circumference of the circle qith radius r. Thus,
[tex]88=2\pi r,\\ \\r=\dfrac{88}{2\pi}=\dfrac{44}{\pi}=\dfrac{44}{\frac{22}{7}}=\dfrac{44}{1}\cdot \dfrac{7}{22}=14\ cm.[/tex]
Thvolume of the sphere can be calculated using formula
[tex]V=\dfrac{4}{3}\pi r^3.[/tex]
Since r=14 cm, we get
[tex]V=\dfrac{4}{3}\cdot \dfrac{22}{7}\cdot 14^3=\dfrac{4\cdot 22\cdot 2\cdot 14^2}{3}=\dfrac{34496}{3}\approx 11499\ cm^3.[/tex]
