Final answer:
The volume of water required to fill the cone-shaped cup to half of its capacity is given as 48π cm³, calculated using the volume formula for a cone with half of the total volume accounted for.
Step-by-step explanation:
To find the volume of water that will fill the cone-shaped cup to half of its capacity, we need to use the formula for the volume of a cone, V = 1/3\u03c0r^2h. Given that the cup has a diameter of 12 cm, the radius (r) is 6 cm. The altitude (h) is given as 8 cm. So, the full volume of the cone would be:
V = 1/3\u03c0(6 cm)^2(8 cm)
V = 96\u03c0 cm^3
Half the volume would be:
V/2 = 48\u03c0 cm^3
Thus, the correct answer is 2) 48\u03c0 cm^3.