I have the answer to the first part of the question, which is What is the volume of Ted's Submarine model. The answer is 490.08=volume. The second part of the question is if 1 inch in the model represents 20 feet in the actual submarine, what is the volume of the actual submarine. The front round part is 3 inch radiusl the middle part is radius 3 inch/length 12 inches; the tail is 3 inch radius/length is 4 inches. Having a problem figuring this part out.
front hemisphere volume is 2/3 pi * 3^3
middle cylinder volume is pi * 3^2 * 12
tail cylinder is pi * 3^2 * 4
Add 'em up. I get 508.93
Maybe I misunderstood the problem.
Anyway, having the volume of the model, the real sub is scaled up by a factor of 20*12 = 240
So, the volume is scaled up by a factor of 240^3
To calculate the volume of the actual submarine, we can use the concept of scaling.
Let's break down the different parts of the submarine model and their dimensions:
1. Front round part: The radius of the front round part in the model is 3 inches. Since 1 inch in the model represents 20 feet in the actual submarine, the radius of the actual submarine's front round part would be (3 inches) * (20 feet/inch) = 60 feet.
2. Middle part: The radius of the middle part in the model is 3 inches, and the length is 12 inches. Following the scaling factor, the radius of the actual submarine's middle part would be (3 inches) * (20 feet/inch) = 60 feet, and the length would be (12 inches) * (20 feet/inch) = 240 feet.
3. Tail: The radius of the tail in the model is 3 inches, and the length is 4 inches. Applying the scaling factor, the radius of the actual submarine's tail would be (3 inches) * (20 feet/inch) = 60 feet, and the length would be (4 inches) * (20 feet/inch) = 80 feet.
To calculate the volume of each part of the submarine, we can use the formula for the volume of a cylinder: V = π * r^2 * h, where V is the volume, π (pi) is a constant approximately equal to 3.14159, r is the radius, and h is the height or length.
For the front round part:
V_front = π * (60 feet)^2 * h_front
For the middle part:
V_middle = π * (60 feet)^2 * h_middle
For the tail:
V_tail = π * (60 feet)^2 * h_tail
To find the volume of the actual submarine, we need to calculate the volumes of each part and add them together:
V_actual = V_front + V_middle + V_tail
Using the formula for the volume of the model that you provided (490.08 = volume in the model), we can set up the equation:
490.08 = π * (3 inches)^2 * h_model
Solving for h_model, we get:
h_model = 490.08 / (π * (3 inches)^2)
With this value of h_model, we can now calculate the volumes of each part in the actual submarine:
V_front = π * (60 feet)^2 * h_model
V_middle = π * (60 feet)^2 * h_model
V_tail = π * (60 feet)^2 * h_model
Finally, adding these volumes together, we find the volume of the actual submarine.