# Question #10176

Oct 13, 2017

Find the volume of the prism, then subtract that amount from the volume of the sphere. The remaining amount will be the volume in between in whatever units.

${V}_{s} = \frac{4}{3} \pi {r}^{3}$

${V}_{p} = l w h$

${V}_{s} = \frac{4}{3} \pi {\left(7\right)}^{3} = \frac{1372 \pi}{3}$

${V}_{p} = \left(4\right) \left(6\right) \left(12\right) = 288$

Volume between sphere and inscribed prism is:

${V}_{s} - {V}_{p} = \frac{1372 \pi}{3} - 288 = \frac{1372 \pi - 864}{3} \approx 1148$ cubic units