Chapter 12, Problem 3CR

To determine

Tofind:The total area and volume of the rectangular solid with dimensions $8$ , $6$ and $5$ .

Answer to Problem 3CR

The total area and volume of the rectangular solid is equal to $236$ square units and 240 cubic units, respectively.

Explanation of Solution

Given information:

The dimensions of the rectangular solid are $8$ , $6$ and $5$ .

Calculation:

Write the formula for the total area of the rectangular solid.

  $\text{Total}\text{area}=2\left(\text{LB}+\text{BH}+\text{HL}\right)$

Where,

• The length is $\text{L}$ .
• The width is $\text{B}$ .
• The height is $\text{H}$ .

Substitute $8$ for $\text{L}$ , $6$ for $\text{B}$ and $5$ for $\text{H}$ in the formula for total area.

  $\begin{array}{c}\text{Total}\text{area}=2\left(8\times 6+6\times 5+5\times 8\right)\\ =2\left(48+30+40\right)\end{array}$

Further simplify.

  $\begin{array}{c}\text{Total}\text{area}=2\left(48+30+40\right)\\ =2\left(118\right)\\ =236\text{square}\text{units}\end{array}$

So, the total area of the rectangular solid is equal to 236 square units.

Write the formula for the volume of the solid.

  $\text{Volume}=\text{LBH}$

Substitute $8$ for $\text{L}$ , $6$ for $\text{B}$ and $5$ for $\text{H}$ in the formula for volume.

  $\begin{array}{c}\text{Volume}=\text{8}\times \text{6}\times \text{5}\\ =\text{240}\text{cubic units}\end{array}$

So, the volume of the rectangular solid is equal to 240 cubic units.

Therefore, the total area and volume of the rectangular solid is equal to $236$ square units and 240 cubic units, respectively.