contestada

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 = __________

Respuesta :

Answer:

[tex](a)s^2\\(b)162=2s^2\\(c)s=9$ ft[/tex]

Step-by-step explanation:

(a)Base Area

Side length of square base=s

Area of a Square of side length s=[tex]s^2$ ft^2[/tex]

(b)

  • Height =6 ft
  • Volume=[tex]162 $ ft^3.[/tex]

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

Substituting the given values, we have:

[tex]162=\frac{1}{3}Xs^2 X 6\\\\162=2s^2[/tex]

(c)Solving the equation derived from (b)

[tex]162=2s^2\\$Divide both sides by 2\\s^2=81\\s^2=9^2\\s=9$ ft[/tex]

Solving this equation shows that s =9 ft.

Otras preguntas