A right pyramid with a square base has a volume of 16 cubic feet. The height is six times the base edge length. What is the height of the pyramid?

Question

I wasn't sure my answers were correct and I'm not quite sure that I did the algebra right. I'd love to compare answers

Answer 1

The volume of a square-based pyramid is

 

V = (1/3)b²h

 

where:

V = volume

b = base length

h = height

 

Use the equation

 

h = 6b    ----->  b = h / 6

 

Then rewriting the formula in terms of h,

 

V = (1/3)(h/6)²h

V = (1/3)(h³/36)

V = h³ / 108

 

108V = h³

 

³√(108V) = h

 

 

Plug in the values to solve for h.

Answer 2

Hi Grace!

 

The volume of a pyramid is V = (1/3)Bh where B is the area of the base and h is the height.

If x is the length of one side of the square base, then B is x^2.

Since the height is six times the base edge length, h = 6x.

 

Substituting these into the formula for volume, as well as the 16, we see that

 

16 = (1/3)(x^2)(6x)

16 = 2x(x^2)

16 = 2x^3

8 = x^3

2 = x

 

So, the height is 6x = 6(2) = 12 feet.

 

Hope this helps!  :)