186k views
2 votes
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

User Rystraum
by
7.3k points

1 Answer

4 votes

Answer:

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

User Hanh
by
8.0k points