Question

12. find the lateral surface area in square centimeters of the solid described in problem 11.11. find the volume in cubic centimeters of a solid whose base is shown in height is 2 m. Dimensions are in meters.

Answer 1

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:

`2\cdot((6\cdot6)/(2))+6\cdot18=144`

To get the volume, multiply this are by the height:

`144\cdot2=288m^3`

Now, let's convert that into cubic centimiters:

`288m^3\cdot\frac{1\cdot10^{6^{}}cm^3}{1m^3}=288\cdot10^6cm^3`

Therefore, the volume of the described solid is:

`288\cdot10^6cm^3`

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:

`6\cdot2+2\cdot12\cdot2+2\cdot8.49\cdot2+18\cdot2=129.96m^2`

Converting this into square centimiters,

`129.96m^2\cdot(1\cdot10^4cm^2)/(1m^2)=1299600cm^2`

We get that the lateral surface area of the solid is:

`1299600cm^2`