11. First, we need to calculate the area of the base.
We have two 6 by 6 triangles, and one 6 by 18 rectangle. This way, the sufrace area of the base is:
[tex]2\cdot(\frac{6\cdot6}{2})+6\cdot18=144[/tex]
To get the volume, multiply this are by the height:
[tex]144\cdot2=288m^3[/tex]
Now, let's convert that into cubic centimiters:
[tex]288m^3\cdot\frac{1\cdot10^{6^{}}cm^3}{1m^3}=288\cdot10^6cm^3[/tex]
Therefore, the volume of the described solid is:
[tex]288\cdot10^6cm^3[/tex]
12. The outline from the base of the solid will be some sort of "walls" when extruded those 2 m up. Now, we'll have:
• A wall that is 6m long and 2m high
,
• Two walls that are 12m long and 2m high
,
• Two walls that are 8.49m long and 2m high
,
• A wall that is 18m long and 2m high
This way, the lateral surface area, in meters, is:
[tex]6\cdot2+2\cdot12\cdot2+2\cdot8.49\cdot2+18\cdot2=129.96m^2[/tex]
Converting this into square centimiters,
[tex]129.96m^2\cdot\frac{1\cdot10^4cm^2}{1m^2}=1299600cm^2[/tex]
We get that the lateral surface area of the solid is:
[tex]1299600cm^2[/tex]
