Answer:
A. [tex]r^{3}[/tex]([tex]\frac{2}{3}[/tex][tex]\pi[/tex] + 8)
Step-by-step explanation:
A composite figure is formed by two or more shapes in contact.
Volume of a cube = [tex]l^{3}[/tex]
where l is the length of its sides.
Given that l = 2r, then;
volume of the cube = [tex](2r)^{3}[/tex]
= 8[tex]r^{3}[/tex]
volume of the cube = 8[tex]r^{3}[/tex]
For a hemisphere, volume = [tex]\frac{2}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
Also,
volume of the hemisphere = [tex]\frac{2}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
So that,
volume of the composite figure = volume of the cube + volume of the hemisphere
= 8[tex]r^{3}[/tex] + [tex]\frac{2}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
= [tex]r^{3}[/tex](8 + [tex]\frac{2}{3}[/tex][tex]\pi[/tex])
volume of the composite figure = [tex]r^{3}[/tex]([tex]\frac{2}{3}[/tex][tex]\pi[/tex] + 8)
