Math CentralQuandaries & Queries


Question from Carl, a student:

A model for a building is 50 centimeters long, 38 centimeters wide, and 225 centimeters tall
on model 1centimeter represents 2.5 meters.
I need to find the volume of the actual building in cubic meters,and the surface area of the building including
ceilings and floors. round to the nearest tenth of a square meter.

Hi Carl,

Let's start by looking at the floor. The dimensions of the model are 50 cm by 38 cm and 1 cm in the model represents 2.5 m in the actual building. Thus the floor of the building is

50 × 2.5 m by 38 × 2.5 m.

Hence the area of the floor of the building is

(50 × 2.5) × (38 × 2.5) = (50 × 38) × 2.52 square metres.

What you should notice here is that the area of the floor of the building is 2.52 times the area of the floor of the model. (The units change from square centimeters to square metres also.)

Find the areas of the four walls and the ceiling of the model in square centimeters and multiply each by 2.52 to calculate the corresponding areas for the building.

How does the volume of the building in square metres compare to the volume of the model in square centimeters?


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