Question 453159: Please help. A model for a building is 50 centimeters long, 38 centimeters wide, and 225 centimeters tall. On the model, 1 centimeter represents 2.5 meters.
1. How tall is the actual building in meters?
2.Determine the volume of the actual building in cubic meters and the surface area of the actual building including ceiling and floor.
Answer by pedjajov(51)   (Show Source):
You can put this solution on YOUR website! Let's mark length, width and height of the model with l, w and h.
Let's mark length, width and height of the actual building with L, W and H.
:
01. If each centimeter on the model represents 2.5 meters on the actual building
then height of 225 centimeters on the model is
:
H = h*2.5= 225*2.5 = 562.5 meters - very tall building :-)
:
02. This model/building is prism with the rectangle for the base so its volume is
:
V = L*W*H
:
L = l*2.5 = 50*2.5 = 125 meters
W = w*2.5 = 38*2.5 = 70 meters
:
V = L*W*H = 125*70*562.5 = 4921875 cubic meters
:
03. Surface area of the building is the sum of areas for all sides:
:
B - 2 bases are ceiling and floor
L1 - 2 lateral sides of the prism with length and height
L2 - 2 lateral sides of the prism with width and height
:
A = 2B+2L1+2L2
A = 2WL+2WH+2LH
A = 2*70*125 + 2*125*562.5 + 2*70*562.5
A = 236875 square meters
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