Final answer:
The remaining solid's total surface area and volume, after hollowing out a conical cavity from a cylinder, can be calculated using geometrical formulas for the volumes of a cylinder and a cone, and by subtracting the conical cavity's base area from the cylinder's base area and adding the lateral surface area.
Step-by-step explanation:
To find the total surface area and volume of the remaining solid after a conical cavity is hollowed out from a solid cylinder, we need to apply the formulas for the volume of a cylinder and a cone, and the areas of their surfaces.
Volume Calculation
The volume of the original cylinder is given by the formula V = πr²h. With a diameter of 1.4 cm, the radius (r) is half of that, so it is 0.7 cm. Plugging the radius and height (h) into the formula gives:
V_cylinder = π * (0.7 cm)² * 2.4 cm.
Next, we calculate the volume of the conical cavity using the formula V = (1/3)πr²h and subtract it from the volume of the cylinder to find the volume of the remaining solid.
Surface Area Calculation
The total surface area includes the area of the top circle minus the area of the circular base of the conical cavity and the lateral surface area of the cylinder which is πdh (d is the diameter of the cylinder and h is the height). Therefore, the correct total surface area is represented by:
SA_total = π(1.4 cm)² - π(1.4 cm)(2.4 cm).
After calculating the respective volumes and areas using these formulas, we can see that the correct answer is option (d).