Answer :
To find the volume of the oblique pyramid with a square base, we need to follow these steps:
1. Determine the area of the base:
- The base of the pyramid is a square with an edge length of [tex]\(5 \, \text{cm}\)[/tex].
- The area of a square is calculated using the formula:
[tex]\[ \text{Area} = \text{edge}^2 \][/tex]
- Plugging in the edge length, we get:
[tex]\[ \text{Area} = 5 \, \text{cm} \times 5 \, \text{cm} = 25 \, \text{cm}^2 \][/tex]
2. Calculate the volume of the pyramid:
- The volume [tex]\(V\)[/tex] of a pyramid is given by the formula:
[tex]\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \][/tex]
- From the problem statement, we know the height of the pyramid is [tex]\(7 \, \text{cm}\)[/tex], and we already calculated the base area as [tex]\(25 \, \text{cm}^2\)[/tex].
- Plugging these values into the volume formula, we get:
[tex]\[ V = \frac{1}{3} \times 25 \, \text{cm}^2 \times 7 \, \text{cm} = \frac{1}{3} \times 175 \, \text{cm}^3 = 58.3333 \, \text{cm}^3 \][/tex]
- This value can be expressed as a fraction:
[tex]\[ V = \frac{175}{3} \, \text{cm}^3 \][/tex]
- Converting this to a mixed number, we get:
[tex]\[ V = 58 \frac{1}{3} \, \text{cm}^3 \][/tex]
Thus, the volume of the pyramid is:
[tex]\[ 58 \frac{1}{3} \, \text{cm}^3 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{58 \frac{1}{3} \, \text{cm}^3} \][/tex]
1. Determine the area of the base:
- The base of the pyramid is a square with an edge length of [tex]\(5 \, \text{cm}\)[/tex].
- The area of a square is calculated using the formula:
[tex]\[ \text{Area} = \text{edge}^2 \][/tex]
- Plugging in the edge length, we get:
[tex]\[ \text{Area} = 5 \, \text{cm} \times 5 \, \text{cm} = 25 \, \text{cm}^2 \][/tex]
2. Calculate the volume of the pyramid:
- The volume [tex]\(V\)[/tex] of a pyramid is given by the formula:
[tex]\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \][/tex]
- From the problem statement, we know the height of the pyramid is [tex]\(7 \, \text{cm}\)[/tex], and we already calculated the base area as [tex]\(25 \, \text{cm}^2\)[/tex].
- Plugging these values into the volume formula, we get:
[tex]\[ V = \frac{1}{3} \times 25 \, \text{cm}^2 \times 7 \, \text{cm} = \frac{1}{3} \times 175 \, \text{cm}^3 = 58.3333 \, \text{cm}^3 \][/tex]
- This value can be expressed as a fraction:
[tex]\[ V = \frac{175}{3} \, \text{cm}^3 \][/tex]
- Converting this to a mixed number, we get:
[tex]\[ V = 58 \frac{1}{3} \, \text{cm}^3 \][/tex]
Thus, the volume of the pyramid is:
[tex]\[ 58 \frac{1}{3} \, \text{cm}^3 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{58 \frac{1}{3} \, \text{cm}^3} \][/tex]
