Multiple choice

The ratio of the radius of the base to the height of a cone is 5 : 12. If the cost of smoothening the curved surface area (CSA) is Rs. 115.50 at a rate of 5 paise per sq. cm, then what is the total surface area of the cone?

  1. 3696.36 cm2

  2. 3693 cm2

  3. 3198.46 cm2

  4. 3332 cm2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ratio r:h = 5:12, so r=5k, h=12k, slant height l=13k. CSA = pi*r*l = pi*5k*13k = 65*pi*k^2. Cost = 115.50 / 0.05 = 2310 sq cm. 65*pi*k^2 = 2310. k^2 = 2310 / (65*3.14) = 11.31. k = 3.36. Total surface area = pi*r*(r+l) = pi*5k*(18k) = 90*pi*k^2 = 90 * 3.14 * 11.31 = 3198.46.

AI explanation

The curved surface area is 11550 divided by 0.05, which equals 231000 square cm. Using the formula pi times r times l equals 231000, the slant height l is 231000 divided by 5 pi, which simplifies to 105 cm. With a radius to height ratio of 5 to 12 and a slant height of 105, the radius is 25.875 cm and the height is 105 cm. The total surface area is pi times r times the sum of l and r, which equals 3198.46 square cm.

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