To find the volume of an oblique pyramid with a square base and given dimensions, we can use the following steps:
1. Determine the area of the square base:
- The formula for the area [tex]\( A \)[/tex] of a square is given by:
[tex]\[
\text{Area} = \text{side length}^2
\][/tex]
- Here, the side length of the square base is 5 cm. So,
[tex]\[
\text{Area} = 5^2 = 25 \text{ cm}^2
\][/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 base area we found is 25 cm[tex]\(^2\)[/tex], and the height of the pyramid is 7 cm. Plugging these values into the formula:
[tex]\[
V = \frac{1}{3} \times 25 \text{ cm}^2 \times 7 \text{ cm}
\][/tex]
3. Perform the multiplication:
- First, multiply the base area by the height:
[tex]\[
25 \text{ cm}^2 \times 7 \text{ cm} = 175 \text{ cm}^3
\][/tex]
- Next, take one-third of this product:
[tex]\[
V = \frac{1}{3} \times 175 \text{ cm}^3 = 58.33333333333333 \text{ cm}^3
\][/tex]
4. Express the volume:
- The volume in decimal form is approximately 58.33333333333333 cm[tex]\(^3\)[/tex].
- Converting this to a mixed number, we have approximately [tex]\( 58 \frac{1}{3} \)[/tex].
Therefore, the volume of the pyramid is [tex]\( 58 \frac{1}{3} \text{ cm}^3 \)[/tex].
The correct option is:
[tex]\[
\boxed{58 \frac{1}{3} \text{ cm}^3}
\][/tex]
