Find the volume of the figure.

Cylinder with a height=8m, radius of 5m, hemisphere sits on top

1 answer

To find the total volume of the figure, we need to calculate the volume of the cylinder and the hemisphere separately and then add them together.

Volume of the cylinder:
V_cylinder = πr^2h
V_cylinder = π(5m)^2(8m)
V_cylinder = 200π m^3

Volume of the hemisphere:
The volume of a hemisphere is given by:
V_hemisphere = (2/3)πr^3

Since the radius of the hemisphere is also 5m, we can substitute it in:
V_hemisphere = (2/3)π(5m)^3
V_hemisphere = (2/3)π(125m^3)
V_hemisphere = (250/3)π m^3

Now, we add the volume of the cylinder and the hemisphere to get the total volume of the figure:
Total Volume = V_cylinder + V_hemisphere
Total Volume = 200π m^3 + (250/3)π m^3
Total Volume = (600π + 250π) m^3
Total Volume = 850π m^3

Therefore, the volume of the figure is 850π cubic meters.