Final answer:
To find the total volume of the ice cream cone, calculate the volume of the cone and hemisphere separately and then add them together. The volume of the cone is 1.461 cm³ and the volume of the hemisphere is 1.767 cm³. The total volume of the ice cream cone is 3.228 cm³.
Step-by-step explanation:
To find the total volume of the ice cream cone, we need to calculate the volume of the cone and the hemisphere separately, and then add them together. Let's start with the cone:
The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height. In this case, the diameter of the cone is equal to its height, so the radius is half the diameter, or 0.75 cm.
Using the formula, we have V = (1/3)π(0.75 cm)^2 × 5.25 cm = 1.461 cm³
Next, let's find the volume of the hemisphere. The formula for the volume of a sphere is V = (4/3)πr^3. Since the hemisphere is a half sphere, we will divide the volume by 2. The radius is also 0.75 cm, so the volume is V = (1/2)(4/3)π(0.75 cm)^3 = 1.767 cm³.
Finally, we add the volume of the cone and the hemisphere: 1.461 cm³ + 1.767 cm³ = 3.228 cm³.