Question

find the surface area and volume of the solid. round each measure to the nearest tenth, if necessary. surface area: in² volume: in³ 6 in. 5 in. 2 in.

Explanation:

Step1: Recall surface - area formula for rectangular prism

The surface - area formula of a rectangular prism is $SA = 2(lw+lh + wh)$, where $l$ is the length, $w$ is the width, and $h$ is the height. Here, $l = 5$ in, $w = 2$ in, and $h = 6$ in.
\[

$$\begin{align*} SA&=2(5\times2 + 5\times6+2\times6)\\ &=2(10 + 30+12)\\ &=2\times52\\ & = 104 \end{align*}$$

\]

Step2: Recall volume formula for rectangular prism

The volume formula of a rectangular prism is $V=lwh$.
\[

$$\begin{align*} V&=5\times2\times6\\ &=60 \end{align*}$$

\]

Answer:

surface area: $104$ in²
volume: $60$ in³