Question

the surface area of the solid shown is 432 square inches and its volume is 576 cubic inches. 12 in. 8 in. 6 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 length, $w$ is width, and $h$ is height. Here, $l = 8$ in, $w = 6$ in, and $h = 12$ in.
\[

$$\begin{align*} SA&=2(8\times6 + 8\times12+6\times12)\\ &=2(48 + 96+72)\\ &=2(216)\\ & = 432 \end{align*}$$

\]

Step2: Recall volume formula for rectangular prism

The volume formula of a rectangular prism is $V=lwh$. Substitute $l = 8$ in, $w = 6$ in, and $h = 12$ in.
\[

$$\begin{align*} V&=8\times6\times12\\ &=48\times12\\ &=576 \end{align*}$$

\]

Answer:

The surface - area is 432 square inches and the volume is 576 cubic inches.