Chapter 15.2, Problem 19PSB

a.

To determine

To find: the lateral surface area of the given pattern.

Answer to Problem 19PSB

  $714.0$ .

Explanation of Solution

Given:

The pattern shown can be folded to form a prism with a rectangular hexagon base.

  

Calculation:

According to the question, the form of the pattern is a prism with a rectangular hexagon base.

Thus, the lateral surface area of the given prism is

  $\begin{array}{l}LSA=17\times 7\times 6\\ LSA=714\end{array}$

Hence, the lateral surface area of the given pattern is $714.0$

b.

To determine

To find: the total surface area of the given pattern.

Answer to Problem 19PSB

  $968.6$ .

Explanation of Solution

Given:

The pattern shown can be folded to form a prism with a rectangular hexagon base.

  

Calculation:

According to the question, the form of the pattern is a prism with a rectangular hexagon base.

Thus, the total surface area of the given prism is sum of the lateral surface area and the area of the hexagonal base.

Now, area of the hexagonal base is

  $\begin{array}{l}S{A}_{HEX}=\frac{1}{2}ap\\ S{A}_{HEX}=\frac{1}{2}\times \frac{7}{2}\sqrt{3}\times 42\\ S{A}_{HEX}=127.31\end{array}$

Thus, the total surface area of the given prism is

  $\begin{array}{l}TSA=LSA+2S{A}_{HEX}\\ TSA=714+2\left(127.31\right)\\ TSA=714+254.6=968.6\end{array}$

Hence, the total surface area of the given pattern is $968.6$

c.

To determine

To find: the volume of the given pattern.

Answer to Problem 19PSB

  $V=2164.2$ .

Explanation of Solution

Given:

The pattern shown can be folded to form a prism with a rectangular hexagon base.

  

Calculation:

According to the question, the form of the pattern is a prism with a rectangular hexagon base.

Thus, the volume of the given prism is

  $\begin{array}{l}V=S{A}_{HEX}\times 17\\ V=127.31\times 17\\ V=2164.2\end{array}$

Hence, the volume of the given pattern is $V=2164.2$