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?​

Answer 1

Height of the building is 32.67 meters.

Explanation:

Volume of a Pyramid =
`(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 =
`[(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 =
`(1058400)/(180* 180)`

h = 32.67 meters

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