Units in Scale Drawings

There are 2.54 cm in an inch, 12 inches in a foot, and 5,280 feet in a mile.

Here is a floor plan of a recreation center.

(1). What is the scale of the floor plan if the actual side length of the square pool is 15 m? Express your answer both as a scale with units and without units.

(2). Find the actual area of the large rectangular pool. Show your reasoning.

(3). The kidney-shaped pool has an area of 3.2 cm² on the drawing. What is its actual area? Explain or show your reasoning.

(4). Square A is a scaled copy of Square B with scale factor 2. If the area of Square A is 10 units2, what is the area of Square B?

(5). Cube A is a scaled copy of Cube B with scale factor 2. If the volume of Cube A is 10 units3, what is the volume of Cube B?

(6). The four-dimensional Hypercube A is a scaled copy of Hypercube B with scale factor 2. If the “volume” of Hypercube A is 10 units4, what do you think the “volume” of Hypercube B is?

Sorting Out Equivalent Scales.

Here are some cards with a scale on each card.

(1). Sort the cards into sets of equivalent scales. Be prepared to explain how you know that the scales in each set are equivalent. Each set should have at least two cards.

(2). Record one of the sets with three equivalent scales and explain why they are equivalent.

If all the sides of the figure above are increased by a scale factor of 4, what will the new area be?

The Empire State Building in New York City is about 1,450 feet high (including the antenna at the top) and 400 feet wide. Andre wants to make a scale drawing of the front view of the Empire State Building on an -inch-by- 11 -inch piece of paper. Select a scale that you think is the most appropriate for the scale drawing.