Answer:
The volume of the top toy is 67.1175 cubic feet
Step-by-step explanation:
The toy top is a composite figure of a cylinder and an hemisphere, the volume of the figure is therefore, the sum of the volume of the cylinder and the hemisphere
The dimensions of the cylinder are;
The height of the cylinder = 6 feet
The diameter of the cylinder, [tex]D_{cylinder}[/tex] = 1.5 feet
Therefore, the radius of the cylinder, [tex]r_{cylinder}[/tex]= 1/2 × [tex]D_{cylinder}[/tex] = 1/2 × 1.5 ft. = 0.75 ft.
The volume of the cylinder = Area of the base × Height = π × [tex]r_{cylinder}^2[/tex] × (The height of the cylinder)
Where;
π = 3.14
∴ The volume of the cylinder = 3.14 × (0.75 ft.)² × 6 ft.= 10.5975 ft.³
The dimensions of the hemisphere are;
The diameter of the hemisphere, [tex]D_{hemispher}[/tex] = 6 feet
Therefore, the radius of the hemisphere, [tex]r_{hemisphere}[/tex]= 1/2 × [tex]D_{hemispher}[/tex] = 1/2 × 6 ft. = 3 ft.
The volume of the hemisphere = 2/3×π×[tex]r_{hemisphere}^3[/tex]
∴ The volume of the hemisphere = 2/3 × 3.14 × (3 ft.)³ = 56.52 ft.³the
The volume of the top toy = The volume of the cylinder + The volume of the hemisphere
∴ The volume of the top toy = 10.5975 ft.³ + 56.52 ft.³ = 67.1175 ft.³.