Chapter 3, Problem 14STP

To determine

The expression that represents the total surface area.

Answer to Problem 14STP

  $\text{Surface area}\text{of}\text{cube}=6s^2,10s^2,14s^2$

Explanation of Solution

Given:

The total surface area of n cubes having a side of s.

  $\text{Surface area}\text{of}\text{cube}=6s^2$

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the total surface area of a tower of n cubes each having a side of s. $\text{Surface area}\text{of}\text{cube}=6s^2$ and then simplify further as shown below,

  $\begin{array}{c}\text{Surface area}\text{of}\text{cube}=6s^2\\ \text{For}\text{n}=1\\ \text{Surface area}\text{of}\text{cube}=6s^2\\ \text{For}\text{n}=2\\ \text{Surface area}\text{of}\text{cube}=5s^2+5s^2\\ =10s^2\\ \text{For}\text{n}=3\\ \text{Surface area}\text{of}\text{cube}=5s^2+4s^2+5s^2\\ =14s^2\\ \end{array}$

Thus, the $\text{Surface area}\text{of}\text{cube}=6s^2,10s^2,14s^2$