Answer:
(a) r = 9 mm
(b) r = 1.5 cm
(c) r = 4.5 ft
Step-by-step explanation:
Volume of a sphere is given as;
[tex]V = \frac{4}{3} \pi r^3[/tex]
where;
V is the volume of the sphere
r is radius of the sphere
Make r the subject of the formula;
[tex]V = \frac{4}{3} \pi r^3\\\\3V = 4\pi r^3\\\\\frac{3V}{4 \pi} = r^3\\\\r = \sqrt[3]{\frac{3V}{4 \pi}}[/tex]
(a) Volume, V = 972π mm³
[tex]r = \sqrt[3]{\frac{3V}{4 \pi}} \\\\r = \sqrt[3]{\frac{3*972 \pi}{4 \pi}}\\\\r = \sqrt[3]{729} \\\\r = 9 \ mm[/tex]
(b) Volume, V = 4.5π cm³
[tex]r = \sqrt[3]{\frac{3V}{4 \pi}} \\\\r = \sqrt[3]{\frac{3*4.5 \pi}{4 \pi}}\\\\r = \sqrt[3]{3.375} \\\\r = 1.5 \ cm[/tex]
(c) Volume, V = 121.5π ft³
[tex]r = \sqrt[3]{\frac{3V}{4 \pi}} \\\\r = \sqrt[3]{\frac{3*121.5 \pi}{4 \pi}}\\\\r = \sqrt[3]{91.125} \\\\r = 4.5 \ ft[/tex]
