Final answer:
The student's classmate's error was in incorrectly calculating the lateral surface area of the cone. The correct lateral area is π(3)(5), not π(5)2. The correct surface area formula for a cone is S.A. = πr2 + πrl. Option B is the correct answer B. The lateral area should have been calculated as Ï(3)(5).
Step-by-step explanation:
The student's classmate has made an error in the calculation of the cone's surface area by not calculating the lateral area correctly. The formula for the surface area (S.A.) of a cone is S.A. = πr2 + πrl where r is the radius of the base, and l is the slant height of the cone.
Option B is the correct answer, as the lateral area should have been calculated as π(3)(5), where 3 is the radius and 5 is the slant height of the cone, obtained using the Pythagorean theorem to find the slant height (l = √(r2 + h2), where h is the height of the cone).
The base area was correctly calculated as π(3)2 = 9π. Therefore, the correct surface area should be the sum of the base area and the lateral surface area, calculated as follows: S.A. = 9π + 15π = 24π.
The error in your classmate's calculation is that they incorrectly calculated the lateral area of the cone. The lateral area of a cone is given by the formula πrℓ where r is the radius of the cone and ℓ is the slant height of the cone. In this case, the correct calculation would be π(3)(5) = 15π.
Option B is the correct answer B. The lateral area should have been calculated as Ï(3)(5).