Multiple choice

Quantity A The curved surface area of a cylinder with radius 3 units and height 7 units. Quantity B The curved surface area of a cone with radius 7 units and height 6 units.

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

CSA Cylinder = 2 * pi * r * h = 2 * pi * 3 * 7 = 42 * pi. CSA Cone = pi * r * l. Slant height l = sqrt(r^2 + h^2) = sqrt(7^2 + 6^2) = sqrt(49 + 36) = sqrt(85) approx 9.22. CSA Cone = pi * 7 * 9.22 = 64.54 * pi. Since 64.54 > 42, Quantity B is greater.

AI explanation

Using the formula for the curved surface area of a cylinder, 2*pi*r*h, Quantity A is 2 * pi * 3 * 7 = 42*pi. Quantity B uses the cone formula, pi*r*l, where the slant height l is sqrt(7^2 + 6^2) = sqrt(85). The area for Quantity B is pi * 7 * sqrt(85), which equals approximately 64.4*pi. Comparing the two values, 64.4*pi is greater than 42*pi, making Quantity B greater.

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