SOLUTION: A right pyramid, 18m high, has a square base measuring 10m by 10m. If the top section 3m high is removed, what is the volume of the remaining frustum?

Algebra ->  Volume -> SOLUTION: A right pyramid, 18m high, has a square base measuring 10m by 10m. If the top section 3m high is removed, what is the volume of the remaining frustum?      Log On


   

Question 1179277: A right pyramid, 18m high, has a square base measuring 10m by 10m. If the top section 3m high is removed, what is the volume of the remaining frustum?
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Volume of the pyramid
V=+%281%2F3%29%2810m%2A10m%29%2A18m
V=+600m%5E3+
If the top section 3m high is removed, we need to deduct the volume the top section v from V=+600m%5E3+
v=%281%2F3%29%2Aa%5E2%2A3m
the side of the square base s the top section is proportional to the side of the square base of right pyramid in same ratio as altitudes



s%2F10m=3m%2F18m
s%2F10m=1%2F6
s=10m%2F6
s=5m%2F3
v=%281%2F3%29%2A%285m%2F3%29%5E2%2A3m
v=%281%2F3%29%2A%2825m%5E2%2F9%29%2A3m
v=%281%2F3%29%2A%2825%2F9%29%2A3m%5E3
v=%2825%2F9%29m%5E3
the volume of the remaining frustum
V%5Bf%5D=+600m%5E3-+%2825%2F9%29m%5E3
V%5Bf%5D=+597.22m%5E3


Answer by ikleyn(52818) About Me  (Show Source):
You can put this solution on YOUR website!
.

You calculate the volume of the large (whole) pyramid first

    V = %281%2F3%29%2A10%5E2%2A18 = 600 m^3.         (1)



From it, you subtract the volume of the small cut pyramid, which is

   %281%2F6%29%5E3%2A600 = 2.778 m^3   (rounded).       (2)   



You will get finally for the volume of the frustum

   V%5Bfrustum%5D = 600 - 2.778 = 577.222 m^3  (rounded).     (3)    ANSWER




      The volume of the small pyramid is  %281%2F6%29%5E3 = 1%2F216  
      of the volume of the large pyramid since they are SIMILAR 
      solid bodies with the coefficient of similarity  1%2F6 = 3%2F18.

Solved.


In solving this simple problem, you do not need to make many boring calculations
if you know this basic and useful property of the volumes of similar solid bodies.