Multiple choice

A solid metallic cube has a side length of 14 cm. The largest possible sphere is carved out from this cube. What is the approximate volume of the material wasted (i.e., the volume of the cube remaining after the sphere is carved out)? (Use π=22/7)

  1. 4204

  2. 1306

  3. 7603

  4. 4003

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Cube volume = 14^3 = 2744. Sphere radius = 7. Sphere volume = 4/3 * 22/7 * 7^3 = 4/3 * 22 * 49 = 4312/3 = 1437.33. Wasted = 2744 - 1437.33 = 1306.67.

AI explanation

The volume of the cube is 14 cubed, which is 2744 cubic centimeters. The largest sphere carved from this cube will have a diameter equal to the side of the cube, making its radius 7 centimeters. The volume of this sphere is (4 divided by 3) times pi times r cubed, which calculates to (4 divided by 3) times (22 divided by 7) times 343, equaling approximately 4312 divided by 3 or roughly 1437.3 cubic centimeters. The wasted material is the difference between the cube's volume and the sphere's volume, which is 2744 minus 1437.3, resulting in approximately 1306.7 cubic centimeters, making the closest option 1306.

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