Question

Find the surface area of the figure in square feet.

Answer 1

The surface area of the figure will be the surface area of the cone plus the surface area of the rectangular prism, minus the area of the base of the cone, therefore:

For the cone:

`\begin{gathered} SAc=\pi r^2+\pi r\sqrt[]{r^2+h^2} \\ \text{Where:} \\ r=3 \\ h=7.6 \\ SAc=\pi(3^2)+\pi(3)\sqrt[]{3^2+7.6^2} \\ SAc=105.2811719ft^2 \end{gathered}`

For the rectangular prism:

`\begin{gathered} SAr=2(lw+lh+wh)_{} \\ \text{where:} \\ l=9 \\ w=12 \\ h=4 \\ SAr=2(9\cdot12+9\cdot4+4\cdot12) \\ SAr=384ft^2 \end{gathered}`

Area of the base of the cone:

`\begin{gathered} Ac=\pi r^2 \\ \text{where:} \\ r=3 \\ Ac=28.27433ft^2 \end{gathered}`

Therefore:

`SA=105.28+384-28.27=460.95ft^2`