Chapter 12.1, Problem 1PSA

a.

To determine

To calculate: The total surface area of a right rectangular prism with dimensions as 15 cm, 5 cm and 10 cm.

Answer to Problem 1PSA

The total surface area of a right rectangular prism is $550c{m}^2$ .

Explanation of Solution

Given information:

l = 15 cm, w = 5 cm and h = 10 cm.

Formula used:

Area of rectangle: $A=l\times w$

l = length of rectangle

w= width of rectangle

Calculation:

  

  $\begin{array}{l}A({▭}_1)=15\times 10=150c{m}^2\\ A({▭}_2)=15\times 5=75c{m}^2\\ A({▭}_3)=5\times 10=50c{m}^2\end{array}$

Total surface area:

  $\begin{array}{l}A(▭)=2A({▭}_1)+2A({▭}_2)+2A({▭}_3)\\ A(▭)=\left(2\times 150\right)+\left(2\times 75\right)+\left(2\times 50\right)\\ A(▭)=300+150+100\\ A(▭)=550c{m}^2\end{array}$

b.

To determine

To find: The total area of a surface having right rectangular prism with dimensions as 12 mm, 7 mm and 3 mm.

Answer to Problem 1PSA

The total area of a surface having right rectangular prism is $282m{m}^2$ .

Explanation of Solution

Given information:

l = 12 mm, w = 7 mm and h = 3 mm.

Formula used:

Area of rectangle: $A=l\times w$

l = length of rectangle

w= width of rectangle

Calculation:

  

  $\begin{array}{l}A({▭}_1)=12\times 7=84m{m}^2\\ A({▭}_2)=12\times 3=36m{m}^2\\ A({▭}_3)=7\times 3=21m{m}^2\end{array}$

Total surface area:

  $\begin{array}{l}A(▭)=2A({▭}_1)+2A({▭}_2)+2A({▭}_3)\\ A(▭)=\left(2\times 84\right)+\left(2\times 36\right)+\left(2\times 21\right)\\ A(▭)=168+72+42\\ A(▭)=282m{m}^2\end{array}$

c.

To determine

To calculate: The total surface area having rectangular prism which is right with dimensions as 18 in, 9 in and 9 in.

Answer to Problem 1PSA

The total area of a surface having right rectangular prism is $810i{n}^2$ .

Explanation of Solution

Given information:

l = 18 in, w = 9 in and h = 9 in.

Formula used:

Area of rectangle: $A=l\times w$

l = length of rectangle

w= width of rectangle

Calculation:

  

  $\begin{array}{l}A({▭}_1)=18\times 9=162i{n}^2\\ A({▭}_2)=18\times 9=162i{n}^2\\ A({▭}_3)=9\times 9=81i{n}^2\end{array}$

Total surface area:

  $\begin{array}{l}A(▭)=2A({▭}_1)+2A({▭}_2)+2A({▭}_3)\\ A(▭)=\left(2\times 162\right)+\left(2\times 162\right)+\left(2\times 81\right)\\ A(▭)=324+324+162\\ A(▭)=810i{n}^2\end{array}$