Let's solve the problem step-by-step.
Given:
- The edge length of the square base of the pyramid is 5 cm.
- The height of the pyramid is 7 cm.
First, we need to find the area of the square base. The formula for the area of a square is:
[tex]\[
\text{Area} = \text{side}^2
\][/tex]
In this case:
[tex]\[
\text{Area} = 5 \, \text{cm} \times 5 \, \text{cm} = 25 \, \text{cm}^2
\][/tex]
Now that we have the area of the base, we can use it to find the volume of the oblique pyramid. The volume [tex]\( V \)[/tex] of a pyramid is calculated using the formula:
[tex]\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\][/tex]
Substituting the given values:
[tex]\[
V = \frac{1}{3} \times 25 \, \text{cm}^2 \times 7 \, \text{cm}
\][/tex]
[tex]\[
V = \frac{1}{3} \times 175 \, \text{cm}^3
\][/tex]
[tex]\[
V = 58.33333333333333 \, \text{cm}^3
\][/tex]
We can express the volume as a proper fraction. Noting that 58.3333... is equivalent to 58 and one-third:
[tex]\[
V = 58 \frac{1}{3} \, \text{cm}^3
\][/tex]
Therefore, the correct answer among the options provided is:
[tex]\[
\boxed{58 \frac{1}{3} \, \text{cm}^3}
\][/tex]
