Question 1.
\(d:\) diameter of the sphere
\(r:\) radius of the sphere:
As we know,
\(r=\dfrac{d}{2}\\ \\ r=\dfrac{15}{2}~\mathrm{in}\)
Formula for the volume of a sphere, given its radius:
\(V=\dfrac{4\pi r^{3}}{3}\\ \\ \\ V=\dfrac{4\pi\cdot (\frac{15}{2})^{3}}{3}\\ \\ \\ V=\dfrac{4\pi}{3}\cdot \dfrac{15^{3}}{8}\\ \\ \\ V=\dfrac{\diagup\!\!\!\! 4 \pi}{3}\cdot \dfrac{(3\cdot 5)^{3}}{\diagup\!\!\!\! 4\cdot 2}\\ \\ \\ V=\dfrac{\pi}{3}\cdot \dfrac{3^{3}\cdot 5^{3}}{2}\\ \\ \\ V=\dfrac{\pi}{\diagup\!\!\!\! 3}\cdot \dfrac{\diagup\!\!\!\! 3\cdot 3^{2}\cdot 5^{3}}{2}\\ \\ \\ V=\pi \cdot \dfrac{9\cdot 125}{2}\\ \\ \\ \boxed{\begin{array}{c} V=\dfrac{1\,125\pi}{2}\mathrm{~in^{3}} \end{array}}\)
Question 2.
\(r=6.8~\mathrm{ft}\)
The volume of a hemisphere is given by
\(V=\dfrac{2\pi r^{3}}{3}\\ \\ \\ V=\dfrac{2\pi\cdot (6.8)^{3}}{3}\\ \\ \\ V=\dfrac{2\pi\cdot 314.432}{3}\\ \\ \\ V \approx \dfrac{2*3.14*314.432}{3}\\ \\ \\ \boxed{\begin{array}{c} V \approx 658,2\mathrm{~ft^{3}} \end{array}}\)
