Multiple choice

The largest possible sphere is carried out a wooden solid cube of side $7$ cm. Find the volume of the wood left. $\left[\text{Use } \displaystyle \pi =\dfrac { 22 }{ 7 }\right]$

  1. $163.3$
  2. $164$
  3. $165$
  4. $170$
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A Correct answer
Explanation

The volume of the cube is 7^3 = 343. The largest sphere inside has a diameter of 7, so radius = 3.5. Volume of sphere = (4/3) * pi * r^3 = (4/3) * (22/7) * (3.5)^3 = 179.66. Wood left = 343 - 179.66 = 163.33.

AI explanation

The volume of the cube is 7^3 = 343 cubic cm, and the volume of the largest possible sphere inside it has a radius of 3.5 cm, calculated as (4/3) * pi * r^3 = (4/3) * (22/7) * 3.5^3. This sphere volume equals 179.67 cubic cm. Subtracting the sphere's volume from the cube's volume gives the remaining wood: 343 - 179.67 = 163.3 cubic cm.

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