Question

please help me find both the surface area and volume of this solid! please explain step by step so I can understand.

Answer 1

To get the surface area of the figure

we will follow the steps below

Step 1: Find the surface area of the pyramid excluding its base

The pyramid has four triangles: 2 triangles are similar while the other two are also similar (They have the same dimensions)

`\begin{gathered} \Rightarrow \\ 2((1)/(2)*3*8)+2((1)/(2)*4*\sqrt[]{21}) \end{gathered}`

=>

`24+4\sqrt[]{21}`

=>

`42.33`

Step 2: Find the surface area of the cuboid excluding its surface

The surface area of the cuboid will be

`8*4+2(3*4)+2(8*3)`

=>

`104`

Total surface area =42.33+ 104 =146.33 square units

Total surface area=146.33 square units

To get the volume

we will have to find the volume of the pyramid and that of the cuboid

To get The volume of the pyramid, we will have to get its height

Then we can then get the height

`\begin{gathered} \text{height}^2=(\sqrt[]{21})^2-4^2 \\ \text{height}=\sqrt[]{5} \end{gathered}`

The volume of the pyramid will be

`\begin{gathered} V=(1)/(3)* base\text{ area}* height \\ V=(1)/(3)*3*8*\sqrt[]{5} \\ V=8\sqrt[]{5} \\ V=17.89 \end{gathered}`

The volume of the cuboid

=>

lxbxh= 8x4x3=96

The volume of the cuboid will be =17.89+96 =113.89 cubic units