Question

PLEASE HELP!!!!

Theater Club Stage Crew

The school's theater club is building sets that will make ordinary students look like giants. The actors need a door, a table, and a stool that will make them look almost twice as tall!

DOOR: actual height is 80 inches and Height on Set is 44 inches

TABLE: actual height is 28 inches

STOOL: actual height is 18 inches

How can the stage manager use the constant of proportionality to find the dimensions of any new props the director requires?

What should the height of a can of fruit juice used as a prop be if its actual height is 7 inches? Show your work.

Any Fast Help is Greatly Appreciated, and Thank You

Answer 1

The stage manager can determine the size of new props by using the constant of proportionality, which is found by dividing the object's set height by its real height. To make the actors appear almost twice their size, the height on set should be about 0.55 times the object's actual height.

Step-by-step explanation:

To find the dimensions of new props, the stage manager can use the constant of proportionality, which in this case can be found by dividing the Height on Set by the actual height of an object. For the door, the constant is 44 inches (Height on Set) / 80 inches (actual height) = 0.55. This constant should apply to all objects to maintain the illusion of actors looking nearly twice their size.

For the can of fruit juice with an actual height of 7 inches, we'd use the constant of proportionality as follows:

• Actual height of juice can = 7 inches
• Height on Set of juice can = Actual height × Constant of proportionality
• Height on Set of juice can = 7 inches × 0.55 = 3.85 inches

Therefore, the stage prop version of the juice can should be 3.85 inches tall to maintain the scale of the set.

Answer 2

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Answer:

a) the constant of proportionality multiplies every actual linear dimension

b) the can should be 3.85 inches high

Step-by-step explanation:

Since the desire is to have students look twice as tall, we expect the constant of proportionality to be 1/2. Instead, we're told that the stage manager is using a height of 44 inches to represent an 80-inch door. This means their constant of proportionality is 44/80 = 0.55.

A) Any new props can be scaled by this factor (0.55) to find their height on set.

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B) A 7-inch can would be scaled to 7·0.55 = 3.85 inches in height.