Answer:
Surface area of the wood to be painted = ([tex]r^{2}[/tex] + r [tex]\sqrt{h^{2} + r^{2} }[/tex] )[tex]\pi[/tex] - 16[tex]\pi[/tex]
Step-by-step explanation:
Surface area of a cone is given as the sum of the surface area and the area of its base.
i.e Surface area = [tex]\pi[/tex][tex]r^{2}[/tex] + [tex]\pi[/tex]Lr
where: L is the length of its slant height and r is the radius.
Applying the Pythagoras theorem,
L = [tex]\sqrt{h^{2} + r^{2} }[/tex]
Thus,
Surface area = [tex]\pi[/tex]r (r + [tex]\sqrt{h^{2} + r^{2} }[/tex] )
The given cylindrical hole has a radius of 4 cm and depth 2 cm.
The area of one of its circular surfaces = [tex]\pi[/tex][tex]r^{2}[/tex]
= [tex]\pi[/tex] × [tex](4)^{2}[/tex]
= 16[tex]\pi[/tex] [tex]cm^{2}[/tex]
The surface area of the piece of wood to be painted = surface area of cone - area of cylindrical circular surface.
Surface area of the wood to be painted = [tex]\pi[/tex]r (r + [tex]\sqrt{h^{2} + r^{2} }[/tex] ) - 16[tex]\pi[/tex]
