a To draw the two pyramids, begin by drawing two parallelograms and a point above each of them. Then, draw segments connecting their respective corners with the points to form a 3-D pyramid shape. Finally, remember to label the height and base length with the given dimensions.
b We are told to write a verbal expression for the difference in the volume between The Great Pyramid in Egypt and the pyramid at the Louvre in France.
Verbalizing the Formula
To verbally express the volume of any pyramid, we should start by verbalizing the given formula.
V= 1/3 B h
Since B is the area of the base, we will also need to verbally express the formula for the area of a square with side s for each pyramid.
B= s^2
Thus, to verbally express the volume of any pyramid with a square base we would need to translate the combined expression, 13*s^2*h.
Algebraic
Verbal
1/3
one third
*
times
s^2
the base length squared
*
times
h
the height
Forming the Verbal Expression
The word difference indicates that we will be subtracting two things. In this case, we will subtract the volume of the pyramid in France V_F from the volume of the pyramid in Egypt V_E.
& V_E-V_F
&The volume of pyramid in Egypt
& minus
&the volume of pyramid in France.
To form the full verbal expression, we will need to substitute the general expression for the volume of a pyramid for both pyramids. Since we are given the base lengths and the heights, we will substitute those into our expression as well.
Verbal
The Volume of Pyramid in Egypt
The Volume of Pyramid in France
one third
one third
one third
times
times
times
the base length squared
230 squared
35.42 squared
times
times
times
the height
146.5
21.64
We can now write our expression.
&One third times230squared, times146.5,
& minus
&one third times35.42squared, times21.64.
c Let's write the verbal expression from Part B algebraically.
&One third times230squared times146.5
& minus
&one third times35.42squared times21.64.
& 1/3* 230^2* 146.5-1/3* 35.42^2* 21.64
Now we can evaluate the expression to find the difference in volume between the two pyramids.
