Multiple choice

Directions: You are given two quantities, Quantity I and Quantity II. Compare the two quantities and choose the correct option accordingly. Quantity I: Magnitude of volume of a cylinder of radius 3.5 m and height 10 m Quantity II: Magnitude of total surface area of a cylinder of radius 3 m and height 20 m

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I = Quantity II

  4. No relation
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Quantity I (Volume of cylinder) = pi*r^2*h = pi*(3.5^2)10 = pi*12.25*10 = 122.5*pi. Quantity II (Total surface area) = 2*pi*r(r+h) = 2*pi*3*(3+20) = 6*pi*23 = 138*pi. 122.5*pi < 138*pi.

AI explanation

Using the volume of a cylinder formula, pi times radius squared times height, Quantity I evaluates to pi times 3.5 squared times 10, which is 122.5 pi. Using the total surface area of a cylinder formula, 2 pi times radius times height plus 2 pi times radius squared, Quantity II evaluates to 2 pi times 3 times 20 plus 2 pi times 3 squared, giving 120 pi plus 18 pi which equals 138 pi. Since 122.5 pi is less than 138 pi, Quantity I is less than Quantity II.

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