Multiple choice

If the curved surface area of a right-circular cone is 10,010 sq. cm and slant height is 91 cm, then find its total surface area.

  1. 27,720 sq. cm

  2. 14,620 sq. cm

  3. 16,930 sq. cm

  4. 13,860 sq. cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Curved surface area = pi * r * l = 10010. l = 91. pi * r * 91 = 10010. r = 10010 / (91 * 22/7) = 10010 / 286 = 35. Total surface area = pi * r * l + pi * r^2 = 10010 + (22/7) * 35^2 = 10010 + 3850 = 13860.

AI explanation

The formula for the curved surface area of a right circular cone is pi*r*l, where l is the slant height. Using the given values, (22/7) * r * 91 = 10010, which simplifies to 286*r = 10010 and gives a radius of 35 centimetres. The total surface area formula is pi*r*(r+l), which calculates to (22/7) * 35 * (35 + 91) = 110 * 126 = 13860 square centimetres.

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