SSAT Math Question 666: Answer and Explanation

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Question: 666

10. Billy Bob's Beans are currently packaged in cylindrical cans that contain 9 servings. The cans have a height of 20 cm and a diameter of 18 cm. Billy Bob wants to introduce a new single-serving can. If he keeps the height of the can the same, what should the diameter of the single-serving can be?

  • A. 3
  • B. 3
  • C. 4.5
  • D. 6

Correct Answer: D

Explanation:

Beware! The question asks for the diameter, not the radius. First, find the volume of the cylinder as it is now. The equation for the volume of a cylinder is V = πr2h. Plug in the values for r and h from the question. The question states that the diameter is 18 cm, so the radius is 9 cm, and the height is 20 cm. The equation will read V = π(92)(20). Simplify to get V = π(81)(20). Do not bother doing all this multiplication yet! Since the question asks for the diameter of a single serving which has the same height, take this volume (the volume of 9 servings) and divide by 9 to find the volume of a single serving can: V = , which simplifies to V = π(9)(20). To find the diameter, isolate the radius: r2 = 9, which means r = 3. Multiply by 2 to find the diameter, so d = 6 cm. The correct answer is (D). Remember, for any question that may seem difficult or time consuming, skip it and come back to it later if you have time!

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