Evaluate the expression [tex]6 s^2[/tex] to find the surface area of a cube with side length [tex]s=3[/tex] ft.
A) [tex]36 ft ^2[/tex]
B) [tex]324 ft ^2[/tex]
C) [tex]54 ft ^2[/tex]
D) [tex]3 ft ^2[/tex]
Answer (1)
Substitute the side length s = 3 into the surface area expression 6 s 2 .
Calculate 3 2 = 9 .
Multiply the result by 6: 6 \tims 9 = 54 .
The surface area of the cube is 54 f t 2 .
Explanation
Problem Analysis We are given the expression 6 s 2 which represents the surface area of a cube, and we are given that the side length s = 3 ft. Our goal is to find the surface area of the cube by evaluating the expression with the given side length.
Substitution First, we substitute the value of s into the expression: 6 s 2 = 6 ( 3 ) 2 .
Evaluate the exponent Next, we evaluate the exponent: 3 2 = 3 × 3 = 9 .
Multiplication Now, we multiply the result by 6: 6 × 9 = 54 .
Final Answer Therefore, the surface area of the cube is 54 square feet. The correct answer is C) 54 f t 2 .
Examples
Understanding surface area is crucial in many real-world applications. For instance, when you're painting a room, you need to calculate the surface area of the walls to determine how much paint to buy. Similarly, in packaging design, knowing the surface area of a box helps determine the amount of material needed. Even in biology, the surface area of cells affects how efficiently they can absorb nutrients and expel waste. These examples show how calculating surface area is not just a math problem, but a practical skill used in various fields.
