Answer:
The side of the base measures 7 yd. The height is 9 yd.
Step-by-step explanation:
V = (1/3)s²h
where s = side of the base, and h = height of the pyramid.
Let s = side of the base.
Then, h = s + 2.
(1/3)(s²)(s + 2) = 147
s³ + 2s² = 441
s³ + 2s² - 441 = 0
The volume is 147 cu yd.
If it were a cube, the volume would be 441 cu yd.
Cubic root of 441 is 7.6, so start with a guess of 7.
s³ + 2s² - 441 = 0
s = 7
7³ + 2(7²) - 441 =
= 343 + 98 - 441
= 0
7 is a root of the equation.
Try 7 yd as the side of the square.
(1/3)(7 × 7)(7 + 9) = 147
Answer: The side of the base measures 7 yd. The height is 9 yd.
