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Geometric Shapes
Question: What threedimensional geometric shape does the first stage of the Trident II look like?
Answer: It looks like a cylinder.
Discuss the second stage, third stage, and nose fairing also.
The first stage section includes the first stage rocket motor, Thrust Vector Control (TVC) system, and the components to initiate the first stage ignition.
Question: If you had to cover the lateral surface area of the first stage with 3 x 5 index cards, what formula would you use to determine how many cards to use?
Answer: Lateral Surface Area (L) = 2πrh
Class Discussion: If you had a cylinder the same size as the first stage of a Trident II that were made of paper, and you cut it down the side and
unfolded it, what would it look like?
   
Answer: It would look approximately like a square. 
Class Discussion: Discuss the unfolded shape of the second stage, and third stage also. The height of the second stage is 7 feet with a radius of 42 inches. The height of the third stage is 8 feet with a radius onethird the size of the first stage. Note: the third stage is inside the nose fairing.

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Application Activity
All students in the group will be given a 3 x 5 index card. Students will tape their cards together in an attempt to model the first stage in scale.
Based on their paper cylinder, the students will divide into teams to estimate how many cards are needed to completely cover the lateral surface area of the first stage.
Team estimates will be recorded.
Task: Use the formula
L = 2πrh to determine the actual number of 3 x 5 index cards needed to cover the lateral surface area of the first stage (pictured below).
  We must convert height to inches
22 ft = 264 inches
L = 2π(42)(264) ≈ 69,668 in^{2}
One index card = 3 (5) = 15 in^{2}
Number of index cards = 69,668/15 ≈ 4,645  
Answer: It would look approximately like a square. 
Task: Use the formula
L = 2πrh to determine the actual number of 3 x 5 index cards needed to cover the lateral surface area of the second and third stages also.
Question: If you were to construct a cylinder to contain the entire missile on board a modern nuclear submarine, how much total volume of the ship's space would the cylinder require?


Answer:
V = Bh r = 3.5 ft h = 44 ft
B = πr^{2} = π(3.5)^{2} = 12.25π ft^{2}
V = 12.25π(44) = 539π ft^{3} ≈ 1,693 ft^{3}

Class Discussion: Why is it important to know the volume of a missile tube when planning the construction of a nuclear powered submarine?
Possible Answers:
To know how many missiles the submarine can carry.
To know how much space is left for other things such as crew living space, engine space, torpedo space, and control space.
Buoyancy considerations of the submarine.