Multiple choice

A manufacturer makes two solid cylindrical metal rods for a machine part. Each rod has a height of 36 centimeters. Rod A has a diameter of 10 centimeters, and Rod B has a diameter that is 40% greater than the diameter of Rod A. What is the volume, in cubic centimeters, of Rod B?

  1. 882π

  2. 1,296π

  3. 1,764π

  4. 7,056π
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rod A: r = 5, h = 36. Volume A = pi * 5^2 * 36 = 900pi. Rod B: diameter is 40% greater, so diameter = 10 * 1.4 = 14. Radius = 7. Volume B = pi * 7^2 * 36 = 49 * 36 * pi = 1764pi.

AI explanation

Rod B has a diameter that is 40 percent greater than Rod A, so its diameter is 1.4 times 10, which is 14 cm, making its radius 7 cm. The volume of a cylinder is calculated as pi times the square of the radius times the height. Substituting the dimensions for Rod B gives pi times 7 squared times 36, which simplifies to pi times 49 times 36. The volume of Rod B is 1764 times pi cm3.

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