Final answer:
To find the C.S.A, T.S.A, and the volume of the cylinder, calculate the radius from the given perimeter of the base, then use formulas for C.S.A (2πrh), T.S.A (2πr² + 2πrh), and volume (πr²h).
Step-by-step explanation:
The subject of this question is the calculation of the curved surface area (C.S.A), the total surface area (T.S.A), and the volume of a cylinder. Given the height of the cylinder (30 cm) and the perimeter of its base (88 cm), we can find the radius first by using the relationship Perimeter = 2πr. We rearrange this to find the radius r = Perimeter / (2π).
Once the radius is determined, the curved surface area is calculated using C.S.A = 2πrh. Since the question provides the perimeter and the height, the C.S.A can be calculated directly from these values: C.S.A = Perimeter × height. In this case, the C.S.A would be equal to 88 cm × 30 cm, which simplifies to 2640 cm².
The total surface area includes the area of the two circular bases plus the C.S.A. Each base has an area of πr², so the T.S.A is T.S.A = 2πr² + 2πrh. With the radius found and the height given, plug these into the formula to calculate the T.S.A.
Finally, the volume of the cylinder is found using the formula V = πr²h. Again, using the found radius and the given height, the formula gives the volume of the cylinder.