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March 25, 2017

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A pyramid has a square base with sides length of b. The height of the pyramid is h. If the pyramid is enlarged by doubling the height while leaving the base unchanged, what is the effect on the volume of the pyramid?
Will the volume triple?
These are my choices:

a.The volume does not change
b.The volume doubles
c.The volume triples
d.The volume quadruples

  • geometry - ,

    Volume of original pyramid = (1/3)π(b^2)h
    Volume of new pyramid = (1/3)π(b^)(2h) = (2/3)π(b^2)h

    How do they compare ?

  • geometry - ,

    Do they double??

  • geometry - ,

    Yes,
    they differ only by the 1/3 vs 2/3
    and 2/3 is twice as large as 1/3

  • geometry - ,

    A pyramid has a volume of 24 and a base area of 12. What is the length of the altitude of the pyramid?

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