Substitute the given values for b into the formula from Part B.
D
d
Use the table you created in Part C.
A
a
Diagram:
B
b
Equation: h=216/b^2
C
c
Table:
b
h
1
216
3
24
6
6
9
2 23
12
1 12
D
d
If bh, then h<6.
Practice makes perfect
a
Let's draw a pyramid with a square base b cm long and a height of h cm.
b
We are asked now to suppose the volume of the pyramid is 72 cm^3 and to write an equation to find the height h. To do so, we will use the fact that the volume of a pyramid is 13 the area of the base times the height.
V=1/3 A h
As the base is a square with a side length of b cm, its area is b^2 cm^2. Since we know the volume, we can now write the equation as follows.
72=1/3* b^2* h
Now let us rearrange our equation to solve for the height h.
We will create a table to show the values of h when b=1, 3, 6, 9, and 12. To do so, we will use the formula h= 216b^2 that we found in part B.
b
h=216/b^2
h
1
216/1^2
216
3
216/3^2
24
6
216/6^2
6
9
216/9^2
2 23
12
216/12^2
1 12
d
In this part, we will write an inequality for the possible lengths of b such that bless than h, we also have that b is less than 6.
b < 6
Finally, we are also asked to write an inequality for the possible lengths of h such that b>h. This time, notice that, if b is greater than h, then h is less than 6. Therefore, we can write the inequality for h as follows.
h < 6
