Answer :
To find the volume of the oblique pyramid with a square base, we can follow these steps:
1. Determine the area of the base:
Since the base is a square with an edge length of \(5 \, \text{cm}\), we calculate the area of the base as follows:
[tex]\[ \text{Base area} = \text{side}^2 = 5 \, \text{cm} \times 5 \, \text{cm} = 25 \, \text{cm}^2 \][/tex]
2. Calculate the volume of the pyramid:
The formula to calculate the volume \(V\) of a pyramid is given by:
[tex]\[ V = \frac{1}{3} \times \text{Base area} \times \text{Height} \][/tex]
Substituting the values we have:
[tex]\[ V = \frac{1}{3} \times 25 \, \text{cm}^2 \times 7 \, \text{cm} = \frac{1}{3} \times 175 \, \text{cm}^3 = \frac{175}{3} \, \text{cm}^3 \][/tex]
3. Convert the volume into a mixed number:
To convert \(\frac{175}{3}\) into a mixed number, we divide 175 by 3:
[tex]\[ 175 \div 3 = 58 \text{ remainder } 1 \][/tex]
Thus,
[tex]\[ \frac{175}{3} = 58 \frac{1}{3} \, \text{cm}^3 \][/tex]
4. Match with the given options:
Among the provided answer choices, the corresponding volume is:
[tex]\[ 58 \frac{1}{3} \, \text{cm}^3 \][/tex]
Therefore, the volume of the pyramid is:
[tex]\[ \boxed{58 \frac{1}{3} \, \text{cm}^3} \][/tex]
1. Determine the area of the base:
Since the base is a square with an edge length of \(5 \, \text{cm}\), we calculate the area of the base as follows:
[tex]\[ \text{Base area} = \text{side}^2 = 5 \, \text{cm} \times 5 \, \text{cm} = 25 \, \text{cm}^2 \][/tex]
2. Calculate the volume of the pyramid:
The formula to calculate the volume \(V\) of a pyramid is given by:
[tex]\[ V = \frac{1}{3} \times \text{Base area} \times \text{Height} \][/tex]
Substituting the values we have:
[tex]\[ V = \frac{1}{3} \times 25 \, \text{cm}^2 \times 7 \, \text{cm} = \frac{1}{3} \times 175 \, \text{cm}^3 = \frac{175}{3} \, \text{cm}^3 \][/tex]
3. Convert the volume into a mixed number:
To convert \(\frac{175}{3}\) into a mixed number, we divide 175 by 3:
[tex]\[ 175 \div 3 = 58 \text{ remainder } 1 \][/tex]
Thus,
[tex]\[ \frac{175}{3} = 58 \frac{1}{3} \, \text{cm}^3 \][/tex]
4. Match with the given options:
Among the provided answer choices, the corresponding volume is:
[tex]\[ 58 \frac{1}{3} \, \text{cm}^3 \][/tex]
Therefore, the volume of the pyramid is:
[tex]\[ \boxed{58 \frac{1}{3} \, \text{cm}^3} \][/tex]
