Ted made a scale model of a submarine for his science class.
a. What is the volume of Ted’s model?
b. If 1 inch in the model represents 20 feet in the actual submarine,
what is the volume of the actual submarine?
front round is 3 inch radius/length 3 inch
cylinder is length 12 inch
tail cone is 3 inch radius/length of 4 inches.
Need help with the secon part. Not sure is I explained it correctly the first time. I think I may have the first part incorrect.
a. sorry ask someone else
b. you cheater
love you <3
To find the volume of Ted's model submarine, we need to calculate the volume of each component separately and then sum them up.
First, let's calculate the volume of the front round section. Since it has a radius of 3 inches, we can use the formula for the volume of a sphere:
V_front round = (4/3) * π * r^3
V_front round = (4/3) * 3.14 * 3^3
V_front round = 113.04 cubic inches (rounded to two decimal places)
Next, let's calculate the volume of the cylinder section. The cylinder has a length of 12 inches and a radius of 3 inches. The formula for the volume of a cylinder is:
V_cylinder = π * r^2 * h
V_cylinder = 3.14 * 3^2 * 12
V_cylinder = 339.12 cubic inches (rounded to two decimal places)
Finally, let's calculate the volume of the tail cone section. Similar to the front round section, it also has a radius of 3 inches. We can use the formula for the volume of a cone:
V_tail cone = (1/3) * π * r^2 * h
V_tail cone = (1/3) * 3.14 * 3^2 * 4
V_tail cone = 37.68 cubic inches (rounded to two decimal places)
Now, let's sum up the volumes of each section to calculate the total volume of Ted's model submarine:
V_total = V_front round + V_cylinder + V_tail cone
V_total = 113.04 + 339.12 + 37.68
V_total = 489.84 cubic inches (rounded to two decimal places)
To find the volume of the actual submarine, we need to scale up the volume of the model using the given scale where 1 inch in the model represents 20 feet in the actual submarine. Since volume is proportional to the cube of the linear scaling factor, we need to multiply the volume of the model by (20^3):
V_actual submarine = V_total * (20^3)
V_actual submarine = 489.84 * (20^3)
V_actual submarine ≈ 31,437,120 cubic feet