Answer :
Answer:
The surface area of the piece of wood to be painted is:
[tex]A = \pi \cdot (R^{2}-16\,cm^{2}) + 2\pi \cdot R \cdot \sqrt{R^{2}+h^{2}}[/tex]
Step-by-step explanation:
The surface area to be painted is equal to the surface area of the cone minus the cross area of the hole. That is:
[tex]A = \pi \cdot R^{2} + 2\pi\cdot R \cdot \sqrt{R^{2}+h^{2}} - \pi \cdot r^{2}[/tex]
[tex]A = \pi \cdot (R^{2}-r^{2}) + 2\pi \cdot R \cdot \sqrt{R^{2}+h^{2}}[/tex]
Where:
[tex]R[/tex] - Radius at the bottom of the cylinder, measured in centimeters.
[tex]h[/tex] - Height of the cylinder, measured in centimeters.
[tex]r[/tex] - Radius of the cylindrical hole, measured in centimeters.
If [tex]r = 4\,cm[/tex], the surface area of the piece of wood to be painted is:
[tex]A = \pi \cdot (R^{2}-16\,cm^{2}) + 2\pi \cdot R \cdot \sqrt{R^{2}+h^{2}}[/tex]