Question

1. what does the b in the prism volume formula ( v = b\times h ) stand for?

a. perimeter of the base
b. breadth of the prism
c. volume of the base
d. area of the base

Explanation:

In the formula \( V = B\times h \) for the volume of a prism, \( V \) represents volume, \( h \) represents height. By the definition of the prism - volume formula, \( B \) stands for the area of the base. A prism's volume is calculated by multiplying the area of its base (\( B \)) by its height (\( h \)). For example, for a rectangular prism with base length \( l \), base width \( w \), and height \( h \), \( B=l\times w \) (area of the rectangular base) and \( V = B\times h=(l\times w)\times h \). Options a (perimeter of the base, which has units of length, while volume has units of cubic length), b (breadth, a linear measure), and c (volume of the base, which is redundant as we are calculating the volume of the whole prism) are incorrect.

Answer:

d. Area of the base