Answer :
ANSWER
The volume is 197.15 cm³
EXPLANATION
We have to find the volume of the cube and then substract the volume of the cylinder inside.
The volume of the cube is the product of its sides:
[tex]V_{\text{cube}}=6\operatorname{cm}\times6\operatorname{cm}\times6\operatorname{cm}=216\operatorname{cm}^3[/tex]The volume of a cylinder is the area of its base multiplied by its height. This cylinder's diameter is 2cm, therefore its radius is 1cm. The area of its base is:
[tex]A_{\text{base}}=\pi\cdot r^2=\pi\cdot(1\operatorname{cm})^2=\pi\cdot1\operatorname{cm}=3.14\operatorname{cm}^2[/tex]The height of the cylinder is the width of the cube: 6cm. The volume of the cylinder is:
[tex]V_{\text{cylinder}}=A_{\text{base}}\cdot h=3.14\operatorname{cm}^2\times6\operatorname{cm}=18.85\operatorname{cm}^3[/tex]Finally, the volume of the composite figure is:
[tex]V_{\text{figure}}=V_{\text{cube}}-V_{\text{cylinder}}=216\operatorname{cm}^3-18.85\operatorname{cm}^3=197.15\operatorname{cm}^3[/tex]