Final answer:
To calculate the total volume of ice cream, you find the volume of the cone, subtract 1/16th of it for the unfilled part, and then add the volume of the hemisphere. The final answer is the combined volume of the filled part of the cone and the hemisphere on top.
Step-by-step explanation:
To find the volume of the ice cream in the cone, we need to calculate the volume of the cone, subtract the unfilled portion, and add the volume of the hemisphere on top. The formula for the volume of a cone is ⅓πr2h where r is the radius and h is the height. Using the given radius of 3 cm and height of 12 cm, the volume of the cone is:
Volume of cone = ⅓π(32)(12) = ⅓π(9)(12) = 36π cm3
We subtract 1/16th of this volume for the unfilled portion:
Unfilled volume = ⅓π(32)(12) ÷ 16 = ⅓π cm3
Next, we calculate the volume of the hemisphere (half of a sphere) using the formula ⅓πr3, with the radius still being 3 cm:
Volume of hemisphere = ⅓π(33) = ⅓π(27) = ⅓π cm3
Now, we combine the volumes and calculate the total ice cream volume:
Total ice cream volume = Volume of cone - Unfilled volume + Volume of hemisphere
Total ice cream volume = 36π - 2π + ⅓π = (36 - 2 + ⅓)π cm3
Total ice cream volume = (34 + ⅓)π cm3