Question

find the lateral area, surface area, and volume of the following figure. leave answer in simplest radical form or in terms of pi. round to the nearest tenth.

Answer 1

The volume of a rectangular prism can be calculated through the formula,

`V=l* w* h`

then,

`\begin{gathered} V=2in*5in*3in \\ V=30in^3 \end{gathered}`

Then, the lateral area of the prism is the area of the vertical faces of the prism,

`\begin{gathered} LA=2*(h* l+h* w) \\ LA=2*(3in*2in+3in*5in) \\ LA=2*(6in^2+15in^2) \\ LA=2*21in^2 \\ LA=42in^2 \end{gathered}`

Then, in order to calculate the surface area add the horizontal areas with the lateral area

`\begin{gathered} SA=42in^2+2(l* w) \\ SA=42in^2+2(5in*2in) \\ SA=42in^2+20in^2 \\ SA=62in^2 \end{gathered}`