Answer: To find the volume of medicine injected using the syringe, we need to calculate the volume displaced by the plunger when it is pushed.
Given data:
Inner diameter of the syringe (d_syringe) = 5.5 mm = 0.55 cm
Inner diameter of the needle (d_needle) = 0.26 mm = 0.026 cm
Plunger pad diameter (d_pad) = 1.2 cm
We can calculate the cross-sectional areas of the syringe, needle, and plunger pad using their respective diameters:
Area of syringe (A_syringe) = π * (d_syringe/2)^2
Area of needle (A_needle) = π * (d_needle/2)^2
Area of plunger pad (A_pad) = π * (d_pad/2)^2
Now, we can find the volume of medicine displaced by the plunger when it is pushed:
Volume displaced = (A_pad - A_needle) * Plunger travel distance
Since the plunger is fully pressed, it moves through the length of the syringe, which is the difference between the initial and final positions of the plunger. The initial position of the plunger is when the syringe is empty (no medicine), and the final position is when the syringe is fully compressed (full of medicine).
Let's proceed with the calculations:
Initial volume of the syringe (empty): V_initial = A_syringe * Syringe length
Final volume of the syringe (full): V_final = A_syringe * (Syringe length - Plunger travel distance)
Volume of medicine displaced = V_final - V_initial
Now, let's plug in the values:
V_initial = π * (0.55 cm/2)^2 * Syringe length
V_final = π * (0.55 cm/2)^2 * (Syringe length - Plunger travel distance)
Volume of medicine displaced = π * (d_pad/2)^2 * (Syringe length - Plunger travel distance) - π * (d_syringe/2)^2 * Syringe length
Finally, we need to convert the volume from cubic centimeters (cm³) to milliliters (mL) since 1 mL = 1 cm³:
Volume of medicine injected (in mL) = Volume of medicine displaced (in cm³) ≈ π * (d_pad/2)^2 * (Syringe length - Plunger travel distance) - π * (d_syringe/2)^2 * Syringe length
Please note that the actual volume of medicine injected may be slightly less than the calculated value due to factors like air bubbles or small residual amounts in the syringe.