Identify every representation with a volume of \(96~\text{cubic}~\text{units}\).
A. A rectangular prism with length \(8~\text{units}\), width \(4~\text{units}\), and height \(3~\text{units}\)
B. A cylinder with radius \(4~\text{units}\) and height \(6~\text{units}\), using \(V~=~\pi~r^{2}h\)
C. A triangular prism with base area \(12~\text{square}~\text{units}\) and height \(8~\text{units}\)
D. The expression \(6~\times~4~\times~4\)
E. A box that holds \(96~\text{unit}~\text{cubes}\) exactly
F. A cylinder with diameter \(4~\text{units}\) and height \(6~\text{units}\), using \(V~=~\pi~r^{2}h\)
What this problem is really about
Test every representation against the target in cubic units. Use three dimensions or base-area times height for prisms, interpret a count of unit cubes directly, and use circular base area times height for cylinders. Preserve pi exactly, and when a diameter is given, halve it before squaring so the radius occupies the correct formula role.