Multiple choice

Directions: In the following item, Quantity I and Quantity II are given. Determine the relationship between the quantities and choose the appropriate option. Quantity I: Area of a circle with radius 7 cm Quantity II: Three times the area of a triangle with base 14 cm and height 7 cm

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II, or No relation
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A Correct answer
Explanation

Quantity I: pi * 7^2 = 49 * 3.14 = 153.86. Quantity II: 3 * (1/2 * 14 * 7) = 3 * 49 = 147. Since 153.86 > 147, Quantity I > Quantity II.

AI explanation

Quantity I is the area of a circle with a radius of 7 centimeters, calculated using the formula pi times radius squared, resulting in 22/7 times 49, which equals 154 square centimeters. Quantity II is three times the area of a triangle, found by multiplying 3 by half the base times the height, resulting in 3 times 1/2 times 14 times 7, which equals 147 square centimeters. Comparing the two results, 154 is strictly greater than 147. Therefore, Quantity I is greater than Quantity II.

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