To find the volume and surface area of a cube with sides of length [tex]\( s = \frac{1}{2} \)[/tex] inch, we can use the following formulas:
1. For the volume of the cube:
[tex]\[
V = s^3
\][/tex]
2. For the surface area of the cube:
[tex]\[
SA = 6s^2
\][/tex]
Let's calculate each step-by-step.
### Step 1: Calculate the Volume
First, we'll calculate the volume [tex]\( V \)[/tex].
Given:
[tex]\[
s = \frac{1}{2} \text{ inch}
\][/tex]
Using the formula for volume:
[tex]\[
V = s^3
\][/tex]
We substitute [tex]\( s = \frac{1}{2} \)[/tex] into the formula:
[tex]\[
V = \left( \frac{1}{2} \right)^3
\][/tex]
Now, evaluate the cube of [tex]\( \frac{1}{2} \)[/tex]:
[tex]\[
\left( \frac{1}{2} \right)^3 = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}
\][/tex]
Therefore, the volume [tex]\( V \)[/tex] of the cube is:
[tex]\[
V = \frac{1}{8} \, \text{cubic inches}
\][/tex]
### Step 2: Calculate the Surface Area
Next, we'll calculate the surface area [tex]\( SA \)[/tex].
Using the formula for surface area:
[tex]\[
SA = 6s^2
\][/tex]
We substitute [tex]\( s = \frac{1}{2} \)[/tex] into the formula:
[tex]\[
SA = 6 \times \left( \frac{1}{2} \right)^2
\][/tex]
Now, evaluate the square of [tex]\( \frac{1}{2} \)[/tex]:
[tex]\[
\left( \frac{1}{2} \right)^2 = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}
\][/tex]
Then multiply by 6:
[tex]\[
SA = 6 \times \frac{1}{4} = \frac{6}{4} = 1.5
\][/tex]
Therefore, the surface area [tex]\( SA \)[/tex] of the cube is:
[tex]\[
SA = 1.5 \, \text{square inches}
\][/tex]
### Conclusion
The volume of the cube with side length [tex]\( \frac{1}{2} \)[/tex] inch is:
[tex]\[
V = \frac{1}{8} \, \text{cubic inches}
\][/tex]
The surface area of the cube with side length [tex]\( \frac{1}{2} \)[/tex] inch is:
[tex]\[
SA = 1.5 \, \text{square inches}
\][/tex]
