Question

A pyramid has a square base and a height of 6 ft. The volume of the pyramid is 162 ft^3. Let s be the length of a side of the pyramid's base.
A) In terms of s, the area of the base is ____________ .
B) The formula for the volume of a pyramid gives the equation ___________.
C) Solving this equation shows that s = __________

Answer 1

Answer:

$(a)s^2\\(b)162=2s^2\\(c)s=9 ft$

Step-by-step explanation:

(a)Base Area

Side length of square base=s

Area of a Square of side length s=$s^2 ft^2$

(b)

• Height =6 ft
• Volume=$162 ft^3.$

Volume of a Pyramid$=\frac{1}{3}X Base Area X Height$

Substituting the given values, we have:

$162=\frac{1}{3}Xs^2 X 6\\\\162=2s^2$

(c)Solving the equation derived from (b)

$162=2s^2\\ Divide both sides by 2\\s^2=81\\s^2=9^2\\s=9 ft$

Solving this equation shows that s =9 ft.