Answer :
The volume of the composite figure is the third option 385.17 cubic centimeters.
Step-by-step explanation:
Step 1:
The composite figure consists of a cone and a half-sphere on top.
We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.
Step 2:
The volume of a cone is determined by multiplying [tex]\frac{1}{3}[/tex] with π, the square of the radius (r²) and height (h). Here we substitute π as 3.1415.
The radius is 4 cm and the height is 15 cm.
The volume of the cone :
[tex]V = \frac{1}{3} \pi r^{2} h = \frac{1}{3} (3.1415)(4^{2} )(15) = 251.32[/tex] cubic cm.
Step 3:
The area of a half-sphere is half of a full sphere.
The volume of a sphere is given by multiplying [tex]\frac{4}{3}[/tex] with π and the cube of the radius (r³).
Here the radius is 4 cm. We take π as 3.1415.
The volume of a full sphere [tex]\frac{4}{3} \pi r^{3} = \frac{4}{3} (3.1415) (4^{3}) = 268.07[/tex] cubic cm.
The volume of the half-sphere [tex]=\frac{1}{2} (268.07) = 134.037[/tex] cubic cm.
Step 4:
The total volume = The volume of the cone + The volume of the half sphere,
The total volume [tex]251.32+134.037 = 385.357[/tex] cub cm. This is closest to the third option 385.17 cubic centimeters.