Final answer:
The volume of the solid, which is a combination of a cylinder and a hemisphere with the same radius of 4 cm, is calculated as 870.96 cm³ by adding the volumes of both shapes.
Step-by-step explanation:
To find the volume of the solid composed of a cylinder and a hemisphere, we will calculate the volumes separately and then add them together. The formula for the volume of a cylinder is V = πr²h.
Applying this formula, the volume of the cylinder with a radius of 4 cm and a height of 12 cm is:
V = π3.142 × (4 cm)² × 12 cm
= 602.88 cm³.
Next, we use the formula for the volume of a hemisphere, which is half the volume of a sphere. The formula for the volume of a sphere is V = ⅔πr³, so the volume of a hemisphere is half of that. Hence, the volume of the hemisphere with radius 4 cm is:
V = ⅔π × (4 cm)³ / 2
= 268.08 cm³.
Adding the two volumes together, the total volume of the solid is:
Volume of cylinder + Volume of hemisphere = 602.88 cm³ + 268.08 cm³
= 870.96 cm³.
This is the combined volume of the cylinder and hemisphere solid.