SOLUTION: A rectangular prism-shaped building with a square base has a radio tower on the roof. The building has a height that is 5 times the height of the tower. The side length of the base

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Question 1172825: A rectangular prism-shaped building with a square base has a radio tower on the roof. The building has a height that is 5 times the height of the tower. The side length of the base of the building is 50 meters less than the height of the building. The volume of the building is 250,000 cubic meters.
Write an equation for the volume of the building in terms of t, the height of the tower.

Found 2 solutions by ewatrrr, greenestamps:
Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!

Hi
let t = height of radio tower
rectangular prism-shaped building with a square base
h = 5t
Square Base:
L = 5t-50
W = 5t -50
V = 5t(5t-50)^2 = 250,000m^3
V = 125t(t-10)(t-10) = 250000
V = t^3 -20t^2 + 100t - 2000 = 0
t = 20m (tossing out extraneous solutions)
Checking our answer:
100(50)(50) = 250000 Checks
Wish You the Best in your Studies.

Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

Given:
height of tower = t
height of building: 5t (5 times the height of the tower)
length and width of building: 5t-50 each (50m less than the height of the building)
volume of building: 250,000 cubic meters

Volume = (length) times (width) times (height).