Question

Find the total outside surface area and the volume of the object in the picture assume that the bases are regular

Answer 1

Given the slant height and the height of the pyramid cap as;

`s=3.2^(\prime),\text{ h=3'}`

Thus, the total surface area of the shape is;

`\begin{gathered} T\mathrm{}S\mathrm{}A=\text{Area of four triangles + Area of four rectangles + area of a square} \\ TSA=4((1)/(2)*2*3.2)+4(2*8)+(2*2) \\ TSA=4(3.2)+4(16)+4 \\ TSA==12.8+64+4 \\ TSA=80.8 \end{gathered}`

Hence, the total outside surface area of the solid object is 80.8 square feet.

Also, the volume of the solid object is;

`\begin{gathered} V=(1)/(3)(\text{(2}*2)(3))+(2*2*8) \\ V=4+32 \\ V=36 \end{gathered}`

Hence, the volume of the solid object is 36 cubic feet.