Answer
The sphere is $.975$% larger.
Work Step by Step
First, let's calculate the original volume of the aluminum sphere.
$$V=\frac{4}{3}(3.14)r^{3}$$ $$V=\frac{4}{3}\times3.14\times(8.75cm/2)^{3}$$ $$V=350.6cm^{3}$$
Then, let's calculate the change in volume due to thermal expansion.
$$\Delta V = bV_{0}\Delta T$$ $$V_{f}-350.6cm^{3}=(75\times10^{-6})(350.6cm^{3})(160^{\circ}C-30^{\circ}C)$$ $$V_{f}=354.0cm^{3}$$
Therefore, the percent change is
$$\frac{354.0mL-350.6mL}{350.6mL}=.975 \%$$
