Multiple choice

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. (only quantity is to be considered) Quantity I : The total surface area of a cone is 1848 square cm. If the slant height is 25 cm more than the radius, then find the volume of the cone Quantity II : A cylinder has height equal to the radius of the sphere having volume 310464 cubic centimetres. The height and the radius of the cylinder are in the ratio 3 : 2 respectively. Find the volume of the cylinder.

  1. Quantity : I > Quantity : II

  2. Quantity : I ≥ Quantity : II

  3. Quantity : I < Quantity : II

  4. Quantity : II ≥ Quantity : I

  5. Quantity I = Quantity II or relation can't be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: TSA of cone = pi*r*(r+l) = 1848. With l = r + 25, pi*r*(2r+25) = 1848. Solving for r gives r=14, l=39, h=sqrt(39^2-14^2)=sqrt(1325) approx 36.4. Volume I approx 7470. Quantity II: Sphere volume = 310464 = 4/3*pi*R^3, so R^3 = 74088, R=42. Cylinder h=42, r=28. Volume II = pi*28^2*42 approx 103683. Thus I < II.

AI explanation

For Quantity I, the total surface area of a cone gives 22 * r * (r + 25) = 1848, which leads to r = 7 cm, a slant height of 32 cm, a height of sqrt(32^2 - 7^2) = sqrt(975) cm, and a volume of roughly 1501 cubic cm. For Quantity II, the sphere volume gives a radius of 42 cm, and using the cylinder ratio 3:2, the cylinder volume is 155232 cubic cm. Since 1501 is less than 155232, Quantity I is less than Quantity II.

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