Multiple choice

The largest sphere is curved out of a cube of side 7 cm. Find the volume of the sphere (Use π=22/7)

  1. 179.65 cm3

  2. 179.64 cm3

  3. 179.66 cm3

  4. 179.68 cm3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The largest sphere that can be carved out of a cube has a diameter equal to the side of the cube. Here, the diameter is 7 cm, so the radius is 3.5 cm. The volume is (4/3) * pi * r^3 = (4/3) * (22/7) * (3.5)^3 = (4/3) * (22/7) * (7/2)^3 = (4/3) * (22/7) * (343/8) = 179.666... cm^3.

AI explanation

The diameter of the largest sphere carved from a cube equals the side of the cube, so the radius of the sphere is 7/2 = 3.5 cm. Using the volume of a sphere formula, V = 4/3*pi*r^3, and substituting pi = 22/7 and r = 3.5 gives 4/3 * (22/7) * (3.5)^3. Calculating this yields 4/3 * 22 * 42.875 / 7 = 1/3 * 4 * 22 * 6.125 = 179.666..., so the volume is 179.66 cubic cm.

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