Answer: [tex]1,475.8mm^{2}[/tex]
Step-by-step explanation:
1. If you join the top part and the bottom part of the figure, you obtain a sphere. Then, you must apply the formula for calculate the surface area of a sphere:
[tex]SA_s=4r^{2}(3.14)[/tex]
Where r is the radius ([tex]r=\frac{10mm}{2}=5mm[/tex])
2. Then:
[tex]SA_s=4(5mm)^{2}(3.14)=314mm^{2}[/tex]
3. The formula for calculate the suface area of the red part, which is a cylinder, is:
[tex]SA_c=2(3.14)(r)(h)[/tex]
Where h is the height (h=32mm)
4. Then:
[tex]SA_c=2(3.14)(5mm)(32mm)=1,004.8mm^{2}[/tex]
5. So, the total surface area is:
[tex]SA_t=314mm^{2}+1,004.8mm^{2}=1,318.8mm^{2}[/tex]
