To find the volume of an oblique pyramid, we can use the formula for the volume of a regular pyramid as well. The volume [tex]\( V \)[/tex] of a pyramid is given by:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
Step 1: Calculate the Area of the Base
The base of the pyramid is a square with an edge length of 5 cm. The area [tex]\( A \)[/tex] of a square is calculated using:
[tex]\[ A = \text{edge length}^2 \][/tex]
So, in this case:
[tex]\[ A = 5 \, \text{cm} \times 5 \, \text{cm} = 25 \, \text{cm}^2 \][/tex]
Step 2: Multiply the Base Area by the Height
The height of the pyramid is given as 7 cm. To find the volume, we need to use the formula for the volume of a pyramid:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
Substituting the values we have:
[tex]\[ V = \frac{1}{3} \times 25 \, \text{cm}^2 \times 7 \, \text{cm} \][/tex]
Step 3: Perform the Multiplication and Division
First, multiply the base area by the height:
[tex]\[ 25 \, \text{cm}^2 \times 7 \, \text{cm} = 175 \, \text{cm}^3 \][/tex]
Then, divide by 3:
[tex]\[ V = \frac{175 \, \text{cm}^3}{3} \approx 58.3333 \, \text{cm}^3 \][/tex]
Therefore, the volume of the pyramid is approximately [tex]\( 58.3333 \, \text{cm}^3 \)[/tex].
In fractional form, this volume is [tex]\( 58 \frac{1}{3} \, \text{cm}^3 \)[/tex].
Thus, the correct answer from the given options is:
[tex]\[ \boxed{58 \frac{1}{3} \, \text{cm}^3} \][/tex]
