Question

In the diagram the sphere touches each face of the cube at one point-the center of each face. if each side of the cube is 7cm, what is a reasonable estimate for the unoccupied volume of the cube?

a: 120cm3
b: 140cm3
c: 160cm3
d: 180cm3

Answer 1

C

Explanation:

Te unoccupied volume (V) of the cube is calculated as

V = volume of cube - volume of sphere

= 7³ -
`(4)/(3)` πr³ ( r is the radius and r = 7 ÷ 2 = 3.5 )

= 343 -
`(4)/(3)` π × 3,5³

= 343 -
`(4)/(3)` π × 42.875

= 343 - 179.59438

= 163.4....

≈ 160 cm³ ( to the nearest 10 cm³ )