Multiple choice

What is the total surface of a right cone of height 14 cm and a circular base of radius 7 cm?

  1. $462\ { cm }^{ 2 }$
  2. $344.35\ { cm }^{ 2 }$
  3. $498.35\ { cm }^{ 2 }$
  4. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total surface area of a cone = pi * r * (r + l), where l = sqrt(r^2 + h^2). r = 7, h = 14, l = sqrt(49 + 196) = sqrt(245) approx 15.65. Area = 3.14 * 7 * (7 + 15.65) = 21.98 * 22.65 approx 497.8. Option C is the closest.

AI explanation

Using the Pythagorean theorem, the slant height is the square root of 14 squared plus 7 squared, which equals the square root of 245 or 7 * sqrt(5) cm. The total surface area of a cone is pi * r * (r + l). Multiplying pi by 7 cm by (7 + 7 * sqrt(5)) cm gives 49 pi * (1 + sqrt(5)), which calculates to approximately 498.35 cm^2.

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