Question

A triangular pyramid has an isosceles triangular base. The base edge of the triangular base is 10

inches and the height of the base is 16 inches. The volume of the pyramid is 480 cubic inches.

What is the height of the pyramid, in inches?

Answer 1

h=94.87

Explanation:

1. Volume of pyramid formula:

`v=(1)/(3)*a^(2)*h`

`a=b*h` Base Edge * Height of Pyramid

2. We have variables:

V = 480, Base Edge = 10, Height of Base = 16 (Inch)

3. Plug into formula + Rearrange:

`(3V)/(h) =(b*h)^(2) [b^(2) *h^(2) ]`

`(3V*b^(2) )/(h) =h^(2)`

`h^(2)=(3*480*10^(2) )/(16)`

`h=√(9000)`

h≅94.868