Scale Factor vs Area and Volume.
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?
Sort Out Equivalent Scales.
Here are some cards with a scale on each card. Each set should have at least two cards.
(2.) Record one of the sets with three equivalent scales and explain why they are equivalent.
Complete Exercise on Finding Equivalent Scales.
(1). 1 cm to ____________ cm
(2). 1 cm to ____________ m
(3). 1 cm to ____________ km
(4). 2 m to ____________ m
(5). 5 cm to ____________ m
(6). ____________ cm to 1,000 m
(7). _____________ mm to 20 m
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.
Which of these scales are equivalent to 3 cm to 4 km? (Recall that 1 inch is 2.54 centimeters.)