Answer:
80π/3 cm³
Step-by-step explanation:
The figure can be decomposed into a hemisphere (top), a cylinder (middle), and a cone (bottom). The heights of each of these are given in the figure. The height of a hemisphere is also its radius, so the applicable radius for each of these parts is 2 cm.
Volume of the hemisphere
The equation for the volume of a sphere is ...
V = 4/3πr³
The volume of our hemisphere is 1/2 that, so is ...
V = 2/3πr³ = (2/3)π(2 cm)³ = (16/3)π cm³
Volume of the cylinder
The equation for the volume of a cylinder is ...
V = πr²h
where r is the radius and h is the height. Using the given values, we find the volume to be ...
V = π(2 cm)²(4 cm) = 16π cm³
Volume of the cone
The equation for the volume of a cone is ...
V = (1/3)πr²h
You will recognize that this is 1/3 the volume of a cylinder of radius r and height h. Our cylinder (above) has the same radius and height as the cone, so the cone's volume is ...
V = (16/3)π cm³
Total volume
The total volume of the figure is the sum of the volumes of the parts:
total = hemisphere volume + cylinder volume + cone volume
total = (16/3)π cm³ + 16π cm³ + (16/3)π cm³
total = (80/3)π cm³ ≈ 83.8 cm³
