Answer
$0.77$ $in$
Work Step by Step
1. Calculate the volume of the sphere from its mass ad density of aluminum:
$V=\frac{m}{p}= \frac{85g}{2.7 g/cm^{3}}= 31.48 cm^{3}$
2. Convert $cm^{3}$ in $in^{3}$ using convertion factor $1cm^{3} = 16.387in^{3}$
$\frac{31.48 cm^{3}}{16.387in^{3}}= 1.92 in^{3}$
3. Rewrite equation of the volume of the sphere in terms of r:
$V=\frac{4\times r^{3} \times π}{3}$
$r=\sqrt[3] \frac{3\times V}{4\times π} = \sqrt[3] \frac{3\times 1.92 in ^{3}}{4\times 3.14} = 0. 77 in$
