Given:
The composite figure consists of a rectangle and a hemisphere.
The length of the rectangle is 11 mm.
The width of the rectangle is 9 mm.
The height of the rectangle is 6 mm.
We need to determine the volume of the composite figure.
Volume of the rectangle:
The volume of the rectangle can be determined using the formula,
[tex]V=length \times width \times height[/tex]
Substituting the values, we get;
[tex]V=11 \times 9 \times 6[/tex]
[tex]V=594 \ mm^3[/tex]
Thus, the volume of the rectangle is 594 mm³
Volume of the half of the cylinder:
The volume of the half of the cylinder is given by the formula,
[tex]V=\frac{\pi r^2 h}{2}[/tex]
Radius of the cylinder = [tex]\frac{9}{2}=4.5[/tex]
Height of the cylinder = 11 mm
Substituting the values, we get;
[tex]V=\frac{(3.14)(4.5)^2(11)}{2}[/tex]
[tex]V=\frac{699.435}{2}[/tex]
[tex]V=349.72[/tex]
Thus,the volume of the half of the cylinder is 349.72 mm³
Volume of the composite figure:
The volume of the composite figure can be determined by adding the volume of the rectangle and the volume of the half of the cylinder.
Thus, we have;
Volume = Volume of rectangle + Volume of half of the cylinder
Substituting the values, we get;
[tex]Volume = 594+349.72[/tex]
[tex]Volume = 943.72[/tex]
Rounding off to the nearest whole number, we get;
[tex]Volume = 944 \ mm^3[/tex]
Thus, the volume of the composite figure is 944 mm³
Hence, Option d is the correct answer.
