Step 1
Write perimeters out
Volume = 523cm^3
[tex]\pi\text{ = }\frac{22}{7}[/tex]Radius , r = ?
Diameter = 2r
Step 2
Next write out formula of volume of sphere
[tex]\text{Volume of sphere = }\frac{4}{3}\text{ }\pi r^3[/tex]Step 3
Next substitute your values
[tex]\begin{gathered} ^{}^{} \\ \text{Volume of a sphere = }\frac{4}{3}\text{ }\pi r^3 \\ 523\text{ = }\frac{4}{3}\text{ }\times\text{ }\frac{22}{7}xr^3 \\ 523\text{ = }\frac{88r^3}{21} \\ \text{next cross multiply} \\ 88r^3\text{ = 523 x 21} \\ 88r^3\text{ = 10983} \\ \text{Divide through by 88} \\ r^3\text{ = }\frac{10983}{88} \\ r^3\text{ = 124.8} \\ r\text{ = }\sqrt[3]{124.8} \\ r\text{ = 4.99cm} \end{gathered}[/tex]Diameter = 2 x r
= 2 x 4.99
= 9.98
= 10cm
