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Answer :
To find the surface area of the wooden pillar, which is shaped like a square prism, we use the given formula for surface area: [tex]\( SA = 2s^2 + 4sh \)[/tex].
Step-by-Step Solution:
1. Understand the Shape and Its Dimensions:
- The base of the prism is a square with side length [tex]\( s = 4 \)[/tex] inches.
- The height of the prism is [tex]\( h = 9 \)[/tex] inches.
2. Formula for Surface Area of a Square Prism:
The surface area (SA) of a square prism includes the area of the two square bases and the four rectangular sides. The formula is:
[tex]\[
SA = 2s^2 + 4sh
\][/tex]
3. Calculate the Area of the Two Square Bases:
- The area of one square base is [tex]\( s^2 = 4^2 = 16 \)[/tex] square inches.
- Since there are two square bases, the total area of the bases is:
[tex]\[
2 \times s^2 = 2 \times 16 = 32 \text{ square inches}
\][/tex]
4. Calculate the Area of the Four Rectangular Sides:
- Each rectangular side has an area of [tex]\( s \times h = 4 \times 9 = 36 \)[/tex] square inches.
- Since there are four identical rectangular sides, the total area of these sides is:
[tex]\[
4 \times (s \times h) = 4 \times 36 = 144 \text{ square inches}
\][/tex]
5. Add the Areas to Get the Total Surface Area:
- Combine the area of the two square bases and the four rectangular sides:
[tex]\[
SA = 32 + 144 = 176 \text{ square inches}
\][/tex]
Therefore, the surface area of the wooden pillar is 176 square inches.
The correct answer is A. 176 square inches.
Step-by-Step Solution:
1. Understand the Shape and Its Dimensions:
- The base of the prism is a square with side length [tex]\( s = 4 \)[/tex] inches.
- The height of the prism is [tex]\( h = 9 \)[/tex] inches.
2. Formula for Surface Area of a Square Prism:
The surface area (SA) of a square prism includes the area of the two square bases and the four rectangular sides. The formula is:
[tex]\[
SA = 2s^2 + 4sh
\][/tex]
3. Calculate the Area of the Two Square Bases:
- The area of one square base is [tex]\( s^2 = 4^2 = 16 \)[/tex] square inches.
- Since there are two square bases, the total area of the bases is:
[tex]\[
2 \times s^2 = 2 \times 16 = 32 \text{ square inches}
\][/tex]
4. Calculate the Area of the Four Rectangular Sides:
- Each rectangular side has an area of [tex]\( s \times h = 4 \times 9 = 36 \)[/tex] square inches.
- Since there are four identical rectangular sides, the total area of these sides is:
[tex]\[
4 \times (s \times h) = 4 \times 36 = 144 \text{ square inches}
\][/tex]
5. Add the Areas to Get the Total Surface Area:
- Combine the area of the two square bases and the four rectangular sides:
[tex]\[
SA = 32 + 144 = 176 \text{ square inches}
\][/tex]
Therefore, the surface area of the wooden pillar is 176 square inches.
The correct answer is A. 176 square inches.
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