Answer :
Let's break down the problem step-by-step to determine the correct expression representing the volume of the composite figure, made up of two identical pyramids:
### Step 1: Calculate the Volume of a Single Pyramid
A pyramid’s volume [tex]\( V \)[/tex] can be calculated using the formula:
[tex]\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \][/tex]
Given data for a single pyramid:
- Base length ([tex]\( l \)[/tex]) = 5 units
- Base width ([tex]\( w \)[/tex]) = 0.25 units
- Height ([tex]\( h \)[/tex]) = 2 units
First, calculate the base area:
[tex]\[ \text{Base area} = \text{length} \times \text{width} = 5 \times 0.25 = 1.25 \, \text{square units} \][/tex]
Using the base area in the pyramid volume formula:
[tex]\[ V = \frac{1}{3} \times 1.25 \times 2 \][/tex]
[tex]\[ V = \frac{1}{3} \times 2.5 \][/tex]
[tex]\[ V = \frac{2.5}{3} \][/tex]
[tex]\[ V \approx 0.833 \, \text{cubic units} \][/tex]
So, the volume of one pyramid is approximately [tex]\( 0.833 \)[/tex] cubic units.
### Step 2: Calculate the Volume of the Composite Figure
The composite figure is made of two such pyramids attached at their bases. Therefore, the total volume is:
[tex]\[ \text{Total Volume} = 2 \times \left(\frac{1}{3} \times 5 \times 0.25 \times 2\right) \][/tex]
### Step 3: Identify the Correct Expression
Among the given options, we need to find the one that appropriately represents our derived equation. The expression matching [tex]\( 2 \times \left(\frac{1}{3} \times 5 \times 0.25 \times 2\right) \)[/tex] is:
[tex]\[ \boxed{2\left(\frac{1}{3}(5)(0.25)(2)\right)} \][/tex]
This expression correctly represents the volume of the composite figure.
### Step 1: Calculate the Volume of a Single Pyramid
A pyramid’s volume [tex]\( V \)[/tex] can be calculated using the formula:
[tex]\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \][/tex]
Given data for a single pyramid:
- Base length ([tex]\( l \)[/tex]) = 5 units
- Base width ([tex]\( w \)[/tex]) = 0.25 units
- Height ([tex]\( h \)[/tex]) = 2 units
First, calculate the base area:
[tex]\[ \text{Base area} = \text{length} \times \text{width} = 5 \times 0.25 = 1.25 \, \text{square units} \][/tex]
Using the base area in the pyramid volume formula:
[tex]\[ V = \frac{1}{3} \times 1.25 \times 2 \][/tex]
[tex]\[ V = \frac{1}{3} \times 2.5 \][/tex]
[tex]\[ V = \frac{2.5}{3} \][/tex]
[tex]\[ V \approx 0.833 \, \text{cubic units} \][/tex]
So, the volume of one pyramid is approximately [tex]\( 0.833 \)[/tex] cubic units.
### Step 2: Calculate the Volume of the Composite Figure
The composite figure is made of two such pyramids attached at their bases. Therefore, the total volume is:
[tex]\[ \text{Total Volume} = 2 \times \left(\frac{1}{3} \times 5 \times 0.25 \times 2\right) \][/tex]
### Step 3: Identify the Correct Expression
Among the given options, we need to find the one that appropriately represents our derived equation. The expression matching [tex]\( 2 \times \left(\frac{1}{3} \times 5 \times 0.25 \times 2\right) \)[/tex] is:
[tex]\[ \boxed{2\left(\frac{1}{3}(5)(0.25)(2)\right)} \][/tex]
This expression correctly represents the volume of the composite figure.
