Multiple choice

To make a conical party cap (right cone), how much of cardboard is required if the radius of the cone is 4 times the height of the cone, and the diameter is 14 cm?

  1. 77 3 17 cm2

  2. 77 2 15 cm2

  3. 77 2 17 cm2

  4. 77 3 15 cm2

  5. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
AI explanation

The radius of the cone is half of the diameter, so r = 14 / 2 = 7 cm. Since the radius is 4 times the height, h = 7 / 4 cm. The slant height l is sqrt(r^2 + h^2) = sqrt(7^2 + (7/4)^2) = sqrt(49 + 49/16) = sqrt(833/16) = 7*sqrt(17)/4 cm. The required cardboard is the curved surface area pi*r*l = (22/7) * 7 * 7*sqrt(17)/4 = 77/2*sqrt(17) cm2. The result is 77/2*sqrt(17) cm2.

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