A hollow spherical container is completely filled with water. A solid cube-shaped block of metal is fully submerged inside it such that the diagonal of the cube is equal to the radius of the sphere. What percentage of the sphere’s volume is occupied by the metal block? (in approximate value)
Show answer & explanation
Correct answer: C
Explanation
Given:
Diagonal of the cube = Radius of the sphere (r)
According to the formula:
Diagonal of the cube = a√3
Volume of the cube = a³
Volume of the sphere = (4/3)πr³
a√3 = r
a = r/√3
Volume of the cube = a³
= (r/√3)³
= r³/(3√3)
Volume of the sphere = (4/3)πr³
Ratio of the volumes
= (r³/(3√3)) / ((4/3)πr³)
= 1/(4π√3)
= 1/(4 × 3.14 × 1.732)
= 1/21.75
= 0.046
Percentage = 0.046 × 100 = 4.6%