Final answer:
To find the total surface area of a cylinder, calculate the curved surface area using the formula A = 2πr², where r is the radius. Then, add the area of the two circular bases to the curved surface area using the formula A = 4πr². Given a curved surface area of 2464 cm² and a height equal to the radius, the total surface area of the cylinder is approximately 4927 cm².
Step-by-step explanation:
To calculate the total surface area of a cylinder, we need to consider the curved surface area and the area of the two circular bases. The curved surface area of the cylinder is given as 2464 cm².
The formula for the curved surface area of a cylinder is A = 2πrh, where A is the curved surface area, π is approximately 3.142, r is the radius, and h is the height.
Since the height is given as equal to the radius in this case, we can simplify the formula to A = 2πr².
Substituting the given value for A, we can solve for r: 2464 cm² = 2πr².
Dividing both sides by 2π, we get r² ≈ 392.69. Taking the square root of both sides, we find that r ≈ 19.82 cm.
Now we can calculate the total surface area of the cylinder.
The formula for the total surface area of a cylinder is A = 2πrh + 2πr². Since the height is equal to the radius, this formula becomes A = 2πr² + 2πr² = 4πr².
Substituting the value of r ≈ 19.82 cm into the formula, we can calculate the total surface area: A ≈ 4π(19.82 cm)² ≈ 4926.99 cm².
Rounding to the nearest whole number, the total surface area of the cylinder is approximately 4927 cm².