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?

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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)   (Show Source): You can put this solution on YOUR website!

Volume of the pyramid


If the top section high is removed, we need to deduct the volume the top section from

the side of the square base the top section is proportional to the side of the square base of right pyramid in same ratio as altitudes











the volume of the remaining frustum




Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.

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

    V =  = 600 m^3.         (1)



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

    = 2.778 m^3   (rounded).       (2)   



You will get finally for the volume of the frustum

    = 600 - 2.778 = 577.222 m^3  (rounded).     (3)    ANSWER




      The volume of the small pyramid is   =   
      of the volume of the large pyramid since they are SIMILAR 
      solid bodies with the coefficient of similarity   = .

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.



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