Question

Pyramid A is a right square pyramid with a height of 100 m and a square base with a perimeter of 356 m. Pyramid B has a square base with a perimeter of 456 m and a height of 215 m. Which pyramid has the greater volume and by how many times as​ great? g

Answer 1

The volume of pyramid B is 3.5 times greater than the volume of pyramid A

Explanation:

The area of squared based a pyramid is given by:

`Area = (1)/(3)*s*s*h`

Where 's' the length of the side of the base and 'h' is the height.

For pyramid A:

h= 100 m

s= 356/4 = 89 m

`Area_A = (1)/(3)*89*89*100\\Area_A=264,033.33\ m^3`

For pyramid B:

h= 215 m

s= 456/4 = 114 m

`Area_B = (1)/(3)*114*114*215\\Area_B=931,380\ m^3`

Pyramid B has a greater volume and the ratio between volumes is:

`(Area_B)/(Area_A) =(931,380)/(264,033.33)\\(Area_B)/(Area_A) =3.5`