The volume of the cone is 104.7 cubic feet. The volume of the half-sphere is 261.8 cubic feet and the area of the entire figure is 366.5 cubic feet.
Step-by-step explanation:
Step 1:
The 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).
The radius is 5 feet and the height is 4 feet.
The volume of the cone = [tex]\frac{1}{3} \pi (5) (5) (4) = 104.719[/tex] cubic feet. Rounding this off, we get 104.7 cubic feet.
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 5 feet.
The volume of a full sphere [tex]= \frac{4}{3} (\pi) r^{3} = \frac{4}{3} (\pi)(5^{3} ) = 523.585[/tex] cubic feet.
Step 4:
The volume of the half-sphere = [tex]\frac{fullspherevolume}{2} = \frac{523.585}{2} =261.792.[/tex]
The volume of the half-sphere is 261.792 cubic feet. Rounding this off, we get 261.8 cubic feet.
Step 5:
The total volume = The cone's volume + The half sphere's volume,
The total volume [tex]= 104.719 + 261.792 = 366.511[/tex] cubic feet. By rounding this off to the nearest tenth we get 366.5 cubic feet.
