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

Answer:

C

Step-by-step explanation:

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

V = volume of cube - volume of sphere

   = 7³ - $\frac{4}{3}$ πr³ ( r is the radius and r = 7 ÷ 2 = 3.5 )

   = 343 - $\frac{4}{3}$ π × 3,5³

   = 343 - $\frac{4}{3}$ π × 42.875

   = 343 - 179.59438

   = 163.4....

    ≈ 160 cm³ ( to the nearest 10 cm³ )