Solution
- The question gives us a composite figure made up of a cylinder and a cube.
- We are required to find the volume of the cylinder and the cube and then use the results to find the volume of the composite figure.
- The formulas needed for this calculation are:
[tex]\begin{gathered} Volume\text{ of Cylinder}=\pi\times r^2\times h \\ where, \\ r=radius\text{ of the cylinder} \\ h=height\text{ of the cylinder} \\ \\ Volume\text{ of Cube}=l^3 \\ where, \\ l=dimension\text{ of the cube} \\ \\ Volume\text{ of Composite figure}=Volume\text{ of Cylinder }+Volume\text{ of Cube} \\ \end{gathered}[/tex]
- With the information above, we can proceed to solve the question
Volume of the Cylinder:
[tex]\begin{gathered} V=\pi\times r^2\times h \\ r=\frac{6}{2}=3\text{ \lparen Since 6cm is the diameter of the cylinder\rparen} \\ h=4 \\ \\ \therefore V=\pi\times3^2\times4 \\ \\ V=36\pi cm^3 \end{gathered}[/tex]
Volume of Cube:
[tex]\begin{gathered} V=l^3 \\ l=9 \\ \therefore V=9^3=729cm^3 \end{gathered}[/tex]
Volume of Composite Figure:
[tex]\begin{gathered} V=36\pi+729 \\ use\text{ }\pi=3.14 \\ \\ V=36\left(3.14\right)+729 \\ \\ V=842.04cm^3 \end{gathered}[/tex]
Final Answer
The volume of the composite shape is 842.04 cm³
