Question

What is the radius of a sphere with the volume of 972pi mm

Answer 1

$\large\text{Hey there!}$

$\mathsf{The\ sphere\ formula\ is: \dfrac{4}{3}\pi\times r^3}$

$\mathsf{Now, that\ we\ have\ our\ formula\ let's\ solve\ for\ the\ equation}$

$\mathsf{So,\ first\ \bf{\underline{DIVIDE}}}\mathsf{\ both\ of\ your\ sides\ by\ \pi}$

$\mathsf{\dfrac{4}{3}r^3=972}\\\\\rightarrow\ \mathsf{r^3=972\times\dfrac{3}{4}}\\\\\mathsf{972\times\dfrac{3}{4}=729}\\\\\mathsf{\rightarrow\ r^3=729}$

$\mathsf{\sqrt[\mathsf{3}]{\mathsf{729}} = 81}\\\\\mathsf{\sqrt{81}=81\div9=9}\\\\\mathsf{\sqrt{81}=9}\\\\\mathsf{r=9}$

$\boxed{\boxed{\mathsf{\bf{Answer: \boxed{\mathsf{radius = \bf{9}}}}}}}\checkmark$

$\large\text{Good luck on your assignment and enjoy your day!}$

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