Final answer:
To calculate the lateral and total surface area of a cylinder, you first determine the radius using the volume formula. Then, use the radius and height in the surface area formulas to get the desired values.
Step-by-step explanation:
The question pertains to finding the lateral surface area and total surface area of a cylinder given its volume and height. To find the lateral surface area, you first need the radius of the cylinder which can be found from the volume formula V = πr²h. Once the radius is determined, you can find the lateral surface area using the formula L = 2πrh.
For the total surface area, you need to add the areas of the two circular bases to the lateral surface area. This can be calculated using the formula T = 2πrh + 2πr². It is a simple matter of plug and play—once you have the radius and height, just apply these to the provided formulas.
In this case, the given volume is 448π cm³ and the height is 7 cm. Substituting these values into the volume of a cylinder formula and solving for r gives radius r, which can then be used to compute both surface areas.