Sure! Let's go through the solution step by step:
### Part (a): Finding the area of the smallest side
To find the area of the smallest side of the block, we need to calculate the area of all three pairs of dimensions and then determine which one is the smallest.
1. The block's dimensions are:
- Length ([tex]\( L \)[/tex]) = 11.3 cm
- Width ([tex]\( W \)[/tex]) = 7.2 cm
- Depth ([tex]\( D \)[/tex]) = 10.4 cm
2. Calculate the area of each pair of dimensions:
- Area of the side with Length and Width:
[tex]\[
\text{Area}_{1} = \text{Length} \times \text{Width} = 11.3 \, \text{cm} \times 7.2 \, \text{cm} = 81.36 \, \text{cm}^2
\][/tex]
- Area of the side with Width and Depth:
[tex]\[
\text{Area}_{2} = \text{Width} \times \text{Depth} = 7.2 \, \text{cm} \times 10.4 \, \text{cm} = 74.88 \, \text{cm}^2
\][/tex]
- Area of the side with Length and Depth:
[tex]\[
\text{Area}_{3} = \text{Length} \times \text{Depth} = 11.3 \, \text{cm} \times 10.4 \, \text{cm} = 117.52 \, \text{cm}^2
\][/tex]
3. Determine the smallest side area:
Comparing the three areas calculated above:
[tex]\[
\text{Smallest side area} = \min(81.36, 74.88, 117.52) = 74.88 \, \text{cm}^2
\][/tex]
### Part (b): Finding the volume of the block
To find the volume of the block, we multiply all three dimensions together.
- Volume ([tex]\( V \)[/tex]):
[tex]\[
V = \text{Length} \times \text{Width} \times \text{Depth} = 11.3 \, \text{cm} \times 7.2 \, \text{cm} \times 10.4 \, \text{cm} = 846.144 \, \text{cm}^3
\][/tex]
### Summary of results:
- Area of the smallest side:
[tex]\[
74.88 \, \text{cm}^2
\][/tex]
- Volume of the block:
[tex]\[
846.144 \, \text{cm}^3
\][/tex]
I hope this explanation helps! Let me know if you have any questions.
