Given:
A composite figure consisting of a cylinder with radius r and height h and a half-sphere with a radius r.
To find:
The total volume of the composite figure.
Solution:
To determine the total volume of the figure, we add the volume of the cylinder and the volume of the half-sphere.
The volume of a cylinder, [tex]V= \pi r^{2} h.[/tex]
The given cylinder has a radius of 3.9 units and a height of 4.3 units. Assume π equals 3.14.
The volume of the cylinder, [tex]V = (3.14)(3.9^{2} )(4.3)= 205.36542[/tex] cubic units.
The volume of a half-sphere, [tex]V= \frac{2}{3} \pi r^{3} .[/tex]
The given half-sphere has a radius of 3.9 units, assume π equals 3.14.
The volume of the half-sphere, [tex]V= \frac{2}{3} (3.14)(3.9^{3} ) = 124.17444[/tex] cubic units.
The total volume of the composite figure [tex]= 205.36542+124.17444=329.53986[/tex] cubic units.
Rounding this off to the nearest hundredth, we get the volume of the cone as 329.54 cubic units.
