Question

Translate each sentence into an equation, inequality, or formula.

The volume V of a pyramid is equal to one third the product of the area of
the base b and its height h.
ial to twenty-five.

Answer 1

The volume of a pyramid is given by the equation V = (1/3)bh, representing one-third the product of the base area (b) and height (h), which is dimensionally consistent.

Step-by-step explanation:

To translate the information about a pyramid's volume into an equation, we use the fact that the volume V of a pyramid is one-third the product of the base area b and its height h. Therefore, the equation takes the form:

V = (1/3)bh

Dimensional analysis helps in verifying the consistency of this formula. As volume is a three-dimensional measurement, its unit could be expressed in cubic units (like cubic meters), while area is a two-dimensional measurement (like square meters), and height is one-dimensional (like meters). Multiplying area (m2) by height (m) and dividing by a constant gives a volume (m3), which confirms our equation is dimensionally consistent.