Answer:
1018 mm²
Step-by-step explanation:
In the given cylinder, the shaded face is its top circular face. Therefore, to find its area, we can use the formula for the area of a circle:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Area of a circle}}\\\\A=\pi r^2\\\\\textsf{where:}\\\phantom{ww}\bullet\; \textsf{$A$ is the area.}\\ \phantom{ww}\bullet\;\textsf{$r$ is the radius.}\end{array}}[/tex]
Given that the radius is 18 mm, we can substitute r = 18 into the formula and solve for A:
[tex]A = \pi \cdot 18^2\\\\A=\pi \cdot 324\\\\A=324\pi\\\\A=1017.87601976...\\\\A=1018\; \sf mm^2\;(nearest\;whole\;number)[/tex]
Therefore, the area of the shaded face of the cylinder is 1018 mm², rounded to the nearest whole number.
