To find the volume of the composite figure made of two identical pyramids, we need to follow these steps:
1. Determine the Base Area of One Pyramid:
- The base area is given by [tex]\(5 \times 0.25\)[/tex].
- Calculating this gives us [tex]\(1.25\)[/tex] square units.
2. Determine the Volume of One Pyramid:
- The formula for the volume of a pyramid is [tex]\(\frac{1}{3} \times \text{base area} \times \text{height}\)[/tex].
- Substituting the base area [tex]\(1.25\)[/tex] and the height [tex]\(2\)[/tex], we get:
[tex]\[
\text{Volume of one pyramid} = \frac{1}{3} \times 1.25 \times 2
\][/tex]
- This evaluates to approximately [tex]\(0.8333\)[/tex] cubic units.
3. Determine the Volume of the Composite Figure:
- Since the composite figure consists of two identical pyramids, we simply multiply the volume of one pyramid by 2:
[tex]\[
\text{Volume of composite figure} = 2 \times 0.8333
\][/tex]
- This results in approximately [tex]\(1.6667\)[/tex] cubic units.
Now, comparing the steps mentioned with the given expressions:
[tex]\[
\frac{1}{2}\left(\frac{1}{3}(5)(0.25)(2)\right) \quad \text{(This expression only considers half of one pyramid's volume)}
\][/tex]
[tex]\[
\frac{1}{2}\left(\frac{1}{3}(5)(0.25)(4)\right) \quad \text{(This expression considers half of the volume of double the height)}
\][/tex]
[tex]\[
2\left(\frac{1}{3}(5)(0.25)(2)\right) \quad \text{(This expression considers the correct volume of two pyramids)}
\][/tex]
[tex]\[
2\left(\frac{1}{3}(5)(0.25)(4)\right) \quad \text{(This expression considers the volume of double the height for two pyramids)}
\][/tex]
Among these, the expression that correctly represents the volume of the composite figure made of two identical pyramids is:
[tex]\[
2\left(\frac{1}{3}(5)(0.25)(2)\right)
\][/tex]
