Answer :
To find the volume of an oblique pyramid with a square base and a given height, follow these steps:
1. Calculate the area of the square base:
The base is a square with an edge length of \(5 \, \text{cm}\).
[tex]\[ \text{Base Area} = \text{side} \times \text{side} = 5 \, \text{cm} \times 5 \, \text{cm} = 25 \, \text{cm}^2 \][/tex]
2. Use the volume formula for a pyramid:
The volume \( V \) of a pyramid is given by:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
Here, the height of the pyramid is \( 7 \, \text{cm} \).
3. Substitute the values into the formula:
[tex]\[ V = \frac{1}{3} \times 25 \, \text{cm}^2 \times 7 \, \text{cm} \][/tex]
4. Perform the multiplications inside the parentheses first:
[tex]\[ 25 \times 7 = 175 \, \text{cm}^3 \][/tex]
5. Divide by 3 to find the volume:
[tex]\[ V = \frac{175}{3} \, \text{cm}^3 \approx 58.333 \, \text{cm}^3 \][/tex]
6. Express the volume as a mixed number:
[tex]\[ \frac{175}{3} = 58 \frac{1}{3} \][/tex]
Therefore, the volume of the pyramid is:
[tex]\[ 58 \frac{1}{3} \, \text{cm}^3 \][/tex]
The correct answer is:
[tex]\[ \boxed{58 \frac{1}{3} \, \text{cm}^3} \][/tex]
1. Calculate the area of the square base:
The base is a square with an edge length of \(5 \, \text{cm}\).
[tex]\[ \text{Base Area} = \text{side} \times \text{side} = 5 \, \text{cm} \times 5 \, \text{cm} = 25 \, \text{cm}^2 \][/tex]
2. Use the volume formula for a pyramid:
The volume \( V \) of a pyramid is given by:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
Here, the height of the pyramid is \( 7 \, \text{cm} \).
3. Substitute the values into the formula:
[tex]\[ V = \frac{1}{3} \times 25 \, \text{cm}^2 \times 7 \, \text{cm} \][/tex]
4. Perform the multiplications inside the parentheses first:
[tex]\[ 25 \times 7 = 175 \, \text{cm}^3 \][/tex]
5. Divide by 3 to find the volume:
[tex]\[ V = \frac{175}{3} \, \text{cm}^3 \approx 58.333 \, \text{cm}^3 \][/tex]
6. Express the volume as a mixed number:
[tex]\[ \frac{175}{3} = 58 \frac{1}{3} \][/tex]
Therefore, the volume of the pyramid is:
[tex]\[ 58 \frac{1}{3} \, \text{cm}^3 \][/tex]
The correct answer is:
[tex]\[ \boxed{58 \frac{1}{3} \, \text{cm}^3} \][/tex]
