Question

what is the formula for the volume of a prism given h = u?
○ v = bu
○ v = pu + 2b
○ $v = \frac{4}{3}\pi r^3$
○ $v = \frac{1}{2}bu$
○ $v = \frac{1}{2}pl + b$

Explanation:

Step1: Recall Prism Volume Formula

The volume \( V \) of a prism is given by the formula \( V = B \times h \), where \( B \) is the area of the base and \( h \) is the height (or length) of the prism.

Step2: Substitute \( h = u \)

Given \( h = u \), substitute \( h \) with \( u \) in the formula. So the formula becomes \( V = B \times u \) or \( V = Bu \).

Step3: Eliminate Other Options

• \( V = pu + 2B \) is the surface area formula for a prism, not volume.
• \( V = \frac{4}{3}\pi r^3 \) is the volume of a sphere.
• \( V = \frac{1}{2}Bu \) is the volume of a pyramid (or cone - like) shape, not a prism.
• \( V = \frac{1}{2}pl + B \) is related to surface area or volume of a different solid (like a pyramid's lateral and base area combination), not a prism.

Answer:

A. \( V = Bu \)