The lateral surface area and the total surface area of a cylinder with base radius 7 m and height 9 m are respectively

To solve the problem of finding the lateral surface area and total surface area of a cylinder, let’s use the given values:

• Radius (r): 7 m
• Height (h): 9 m

Step 1: Calculate the Lateral Surface Area of Cylinder

The formula to find the lateral surface area of cylinder is:

        Lateral Surface Area = 2πrh

Substituting the given values:

        Lateral Surface Area = 2 × π × 7 × 9
                            = 2 × (22/7) × 7 × 9
                            = 396 m²

Thus, the lateral surface area of cylinder is 396 m².

Step 2: Calculate the Total Surface Area of Cylinder

The formula to find the total surface area of a cylinder is:

        Total Surface Area = 2πr(r + h)

Substituting the given values:

        Total Surface Area = 2 × π × 7 × (7 + 9)
                           = 2 × (22/7) × 7 × 16
                           = 44 × 16
                           = 704 m²

Hence, the total surface area of the cylinder is 704 m².

Conclusion

The problem involves using the formulas for the lateral surface area of cylinder and total surface area effectively. Using the given radius and height, the lateral surface area of cylinder is 396 m², and the total surface area is 704 m².