Question

the diagram shows a cube with side length ( b ).

1. press continue to divide the cube into six congruent right square pyramids.
2. the pyramid has height ( h = \frac{b}{2} ). because the volume of the cube is ( v_c = b^3 ), the volume of the pyramid is ( v_p = \frac{1}{6}b^3 ). press continue to remove the cube and examine the volume of the pyramid.
3. because ( h = \frac{b}{2} ), we know that ( b = ) dropdown with options ( \frac{1}{2}h ), ( h ), ( 2h )

Explanation:

Step1: Start with the given equation

We are given \( h=\frac{b}{2} \). We need to solve for \( b \) in terms of \( h \).

Step2: Multiply both sides by 2

To isolate \( b \), we multiply both sides of the equation \( h = \frac{b}{2} \) by 2. This gives us \( 2\times h=2\times\frac{b}{2} \), which simplifies to \( b = 2h \).

Answer:

\( 2h \) (corresponding to the option "2h" in the dropdown)