Final answer:
The volume of a cone-shaped paper cup with a height of 12 cm and diameter of 10 cm is approximately 314.16 cubic centimeters, calculated using the cone volume formula V = 1/3πr²h.
Step-by-step explanation:
The question asks for the volume of a cone-shaped paper cup with a height of 12 centimeters and a diameter of 10 centimeters. To find the volume of a cone, we use the formula:
V = ⅓πr²h
First, we need to calculate the radius of the cone. Since the diameter is given as 10 centimeters, the radius (r) is half of that, so r = 5 centimeters. Plugging the values into the formula, we get:
V = ⅓π(5 cm)²(12 cm)
V = ⅓π(25 cm²)(12 cm)
V = 100π cm³
V ≈ 314.16 cm³ (using π ≈ 3.14)
Therefore, the volume of the cone-shaped paper cup is approximately 314.16 cubic centimeters.