Multiple choice

The height of a cone is 24 cm and the area of the base is 154 cm2. What is the curved surface area (in cm2) of the cone?

  1. 484

  2. 550

  3. 525

  4. 515
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Base area = pi * r^2 = 154, so r^2 = 154 * 7 / 22 = 49, r = 7. Height h = 24. Slant height l = sqrt(r^2 + h^2) = sqrt(49 + 576) = sqrt(625) = 25. Curved surface area = pi * r * l = (22/7) * 7 * 25 = 550.

AI explanation

Using the area of the base, pi times radius squared equals 154, and using 22 divided by 7 for pi, the radius calculates to 7 cm. The slant height of the cone is found using the Pythagorean theorem: the square root of (24 squared plus 7 squared), which equals 25 cm. The curved surface area is pi times radius times slant height, giving 22 divided by 7 times 7 times 25, which equals 550 square cm.

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