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,

$V=l\times w\times h$

then,

$\begin{gathered} V=2in\times5in\times3in \\ V=30in^3 \end{gathered}$

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

$\begin{gathered} LA=2\times(h\times l+h\times w) \\ LA=2\times(3in\times2in+3in\times5in) \\ LA=2\times(6in^2+15in^2) \\ LA=2\times21in^2 \\ LA=42in^2 \end{gathered}$

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

$\begin{gathered} SA=42in^2+2(l\times w) \\ SA=42in^2+2(5in\times2in) \\ SA=42in^2+20in^2 \\ SA=62in^2 \end{gathered}$