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A cone has radius 3 and height 4. Your classmate calculates its surface area as shown:

S.A.=π(5)²+π(3)²=25π+9π=3π. Explain your classmate's error.

A. The lateral area should have been calculated as Ï(3)(4).
B. The lateral area should have been calculated as Ï(3)(5).
C. The lateral area should have been calculated as Ï(4)(5).
D. The base area should have been calculated as Ï(1.5)²

1 Answer

7 votes

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).

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