Multiple choice

Directions: In this question, two quantities are given, one as 'Quantity 1' and another as 'Quantity 2'. You have to determine the relationship between the two quantities and choose the appropriate option. The ratio of the total surface area of a cone to the curved surface area of the cone is 13 : 10. Quantity 1: Curved surface area of the cone if the sum of the radius and the slant height of the cone is 13 cm Quantity 2: Curved surface area of the cone if the radius of the cone is 6 cm

  1. Quantity 1 > Quantity 2

  2. Quantity 1 ≥ Quantity 2

  3. Quantity 1 < Quantity 2

  4. Quantity 2 ≥ Quantity 1

  5. Quantity 1 = Quantity 2 or Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total surface area = pi*r*(r+l) and curved surface area = pi*r*l. Ratio (r+l)/l = 13/10 implies 10r + 10l = 13l, so 10r = 3l or l = (10/3)r. Quantity 1: r+l=13, so r + (10/3)r = 13 => (13/3)r = 13 => r=3, l=10. CSA = pi*3*10 = 30pi. Quantity 2: r=6, so l = (10/3)*6 = 20. CSA = pi*6*20 = 120pi. 30pi < 120pi.

AI explanation

The ratio of total surface area to curved surface area is pi times r times l plus r divided by pi times r times l, which simplifies to l plus r over l equaling 13 over 10, meaning the radius r is 0.3 times l. For Quantity 1, since r plus l is 13, substituting r gives 1.3 times l equaling 13, so l equals 10 and the curved surface area is 3 times pi times 30, equaling 90 times pi. For Quantity 2, since r equals 6, l equals 20, making the curved surface area 6 times pi times 20, equaling 120 times pi. Comparing the two shows Quantity 1 is less than Quantity 2. Quantity 1 is less than Quantity 2.

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