Multiple choice

If a rectangular block (4 × 4 × 10) inches is placed inside a right circular cylinder of radius 3 inches and height 10 inches, the volume of the unoccupied portion of the cylinder is how many cubic inches?

  1. (6π - 16) cubic inches

  2. 60π cubic inches

  3. (160π - 30) cubic inches

  4. (90π - 160) cubic inches

  5. None of these
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D Correct answer
Explanation

The volume of the cylinder is pi * r^2 * h = pi * 3^2 * 10 = 90pi. The volume of the rectangular block is 4 * 4 * 10 = 160. The unoccupied volume is 90pi - 160.

AI explanation

The volume of the right circular cylinder is pi times 3 squared times 10, giving 90 pi. The volume of the rectangular block is 4 times 4 times 10, which is 160. The unoccupied portion is the difference between the cylinder volume and the block volume. The volume is (90 pi minus 160) cubic inches.

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