To determine the volume of the oblique pyramid with a square base, we need to follow these steps:
1. Determine the area of the square base:
The edge length of the square base is [tex]\( 5 \)[/tex] cm. The area [tex]\( A \)[/tex] of a square is calculated using the formula:
[tex]\[
A = \text{side}^2
\][/tex]
For this pyramid:
[tex]\[
A = 5^2 = 25 \, \text{cm}^2
\][/tex]
2. Calculate the volume of the pyramid:
The formula for the volume [tex]\( V \)[/tex] of a pyramid is:
[tex]\[
V = \frac{1}{3} \times \text{base area} \times \text{height}
\][/tex]
The height [tex]\( h \)[/tex] of the pyramid is [tex]\( 7 \)[/tex] cm, and the base area we previously computed is [tex]\( 25 \, \text{cm}^2 \)[/tex]. Therefore:
[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]\[
V = 58.333333333 \, \text{cm}^3
\][/tex]
3. Identify the closest answer option:
The volume of the pyramid is [tex]\( 58.333333333 \, \text{cm}^3 \)[/tex], which can be expressed as a mixed number for matching with the given options:
[tex]\[
V = 58 \frac{1}{3} \, \text{cm}^3
\][/tex]
Given the options:
- [tex]\( 11 \frac{2}{3} \, \text{cm}^3 \)[/tex]
- [tex]\( 43 \frac{3}{4} \, \text{cm}^3 \)[/tex]
- [tex]\( 58 \frac{1}{3} \, \text{cm}^3 \)[/tex]
- [tex]\( 87 \frac{1}{2} \, \text{cm}^3 \)[/tex]
The closest match is [tex]\( 58 \frac{1}{3} \, \text{cm}^3 \)[/tex].
Hence, the volume of the pyramid is:
[tex]\[
\boxed{58 \frac{1}{3} \, \text{cm}^3}
\][/tex]
