Volume Problem Solving | Brilliant Math & Science Wiki Since the volume of a hemisphere is half the volume of a a sphere of the same radius, the total volume for this problem is. 1 3 π r 2 h + 1 2 ⋅ 4 3 π r 3. \frac13 \pi r^2 h + \frac12 \cdot \frac43 \pi r^3. 3 1 π r 2 h + 2 1 ⋅ 3 4 π r 3. With height h = 10 h =10 h = 1 0, and diameter d = 6 d = 6 d = 6 or radius r = d 2 = 3 r = \frac d2 ...