Answer :
To determine the correct expression that represents the volume of the pyramid, let's go through the steps clearly:
### Step-by-Step Solution
1. Identify Given Values:
- The area of the base of the pyramid, \( A \), is \( 5.2 \, \text{cm}^2 \).
- The height of the pyramid, \( h \), is given in centimeters (cm).
2. Recall the Volume Formula for a Pyramid:
The volume \( V \) of a pyramid is given by the formula:
[tex]\[ V = \frac{1}{3} \times \text{(Base Area)} \times \text{Height} \][/tex]
3. Substitute the Given Values into the Formula:
- Base Area, \( A = 5.2 \, \text{cm}^2 \)
- Height, \( h \, \text{cm} \)
Therefore, substituting these values into the volume formula:
[tex]\[ V = \frac{1}{3} \times 5.2 \, \text{cm}^2 \times h \, \text{cm} \][/tex]
4. Combine the Terms:
Combining the terms, we get:
[tex]\[ V = \frac{1}{3} \times 5.2 \times h \, \text{cm}^3 \][/tex]
This matches the option:
[tex]\[ \boxed{\frac{1}{3}(5.2) h \, \text{cm}^3} \][/tex]
### Conclusion:
The expression that correctly represents the volume of the pyramid is:
[tex]\[ \frac{1}{3}(5.2) h \, \text{cm}^3 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{\frac{1}{3}(5.2) h \, \text{cm}^3} \][/tex]
### Step-by-Step Solution
1. Identify Given Values:
- The area of the base of the pyramid, \( A \), is \( 5.2 \, \text{cm}^2 \).
- The height of the pyramid, \( h \), is given in centimeters (cm).
2. Recall the Volume Formula for a Pyramid:
The volume \( V \) of a pyramid is given by the formula:
[tex]\[ V = \frac{1}{3} \times \text{(Base Area)} \times \text{Height} \][/tex]
3. Substitute the Given Values into the Formula:
- Base Area, \( A = 5.2 \, \text{cm}^2 \)
- Height, \( h \, \text{cm} \)
Therefore, substituting these values into the volume formula:
[tex]\[ V = \frac{1}{3} \times 5.2 \, \text{cm}^2 \times h \, \text{cm} \][/tex]
4. Combine the Terms:
Combining the terms, we get:
[tex]\[ V = \frac{1}{3} \times 5.2 \times h \, \text{cm}^3 \][/tex]
This matches the option:
[tex]\[ \boxed{\frac{1}{3}(5.2) h \, \text{cm}^3} \][/tex]
### Conclusion:
The expression that correctly represents the volume of the pyramid is:
[tex]\[ \frac{1}{3}(5.2) h \, \text{cm}^3 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{\frac{1}{3}(5.2) h \, \text{cm}^3} \][/tex]
