The Pyramid Arena in Memphis, Tennessee is about 98 meters tall and has a square base with a side length of about 180 meters. A prism-s

Question

The Pyramid Arena in Memphis, Tennessee is about 98 meters tall
and has a square base with a side length of about 180 meters. A prism-shaped
building has the same square base as the Pyramid Arena. What is the height of
the building if it has the same volume as the Pyramid Arena?​

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Eva 1 month 2021-10-13T09:34:59+00:00 1 Answer 0 views 0

Answers ( )

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    2021-10-13T09:36:52+00:00

    Answer:

    Height of the building is 32.67 meters.

    Step-by-step explanation:

    Volume of a Pyramid = \frac{1}{3}(\text{Area of the rectangular base})(\text{Height})

    Side of the square base of the Memphis pyramid = 180 m

    Height of the pyramid = 98 meters

    Volume = [\frac{1}{3}(180)^2](98)

                 = 1058400 cubic meters

    Another building having the same base and volume, is in the shape of a prism.

    Therefore, Volume of the pyramid = volume of the building(prism) = 1058400 cubic meters

    Volume of the prism = (Area of the base) × height

    1058400 = (180)²h

    h = \frac{1058400}{180\times 180}

    h = 32.67 meters

    Therefore, height of the building in the prism shape is 32.67 meters.  

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