✓ 1. Press Continue to divide the cube into six congruent right square pyramids.
✓ 2. The pyramid has height #&h = \frac {b}{\sf 2}#&. Because the volume of the cube is #&V_c = b^{\sf 3}#&, the volume of the pyramid is #&V_p = \frac{\sf 1}{\sf6}b^{\sf 3}#&.
Press Continue to remove the cube and examine the volume of the pyramid.
✓ 3. Because #&h = \frac {b}{\sf 2}#&, we know that b =
.
✓ 4. The volume of the pyramid is #&V_p = \frac{\sf 1}{\sf 6}(b)(b)(b)#&.
Substituting for the first b in this equation, #&V_p = \frac{\sf 1}{\sf6}#&
.
✓ 5. Therefore the volume of the pyramid is
#&V_p = \frac{\sf 1}{\sf 6}(2h)(b)(b),#& or
#&V_p = \frac{\sf 1}{\sf 3}hb^2.#&
Letting the area of the base #&B = b^2,#& the volume of the pyramid is #&V_p = \frac{\sf 1}{\sf 3}Bh#&.