To find the volume of an oblique pyramid with a square base, we use the formula for the volume of a pyramid, which is:
[tex]\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \][/tex]
First, we'll determine the area of the base. Since the pyramid has a square base, the area of the base ([tex]\( \text{base area} \)[/tex]) is given by:
[tex]\[ \text{base area} = \text{edge length}^2 \][/tex]
The edge length of the square base is 5 cm. Therefore:
[tex]\[ \text{base area} = 5 \, \text{cm} \times 5 \, \text{cm} = 25 \, \text{cm}^2 \][/tex]
Next, we use the height of the pyramid in the volume formula. The height of the pyramid is given as 7 cm. Plugging in the values for the base area and the height into the volume formula:
[tex]\[ V = \frac{1}{3} \times 25 \, \text{cm}^2 \times 7 \, \text{cm} \][/tex]
Now we calculate the volume step-by-step:
[tex]\[ V = \frac{1}{3} \times 25 \times 7 \][/tex]
[tex]\[ V = \frac{1}{3} \times 175 \][/tex]
[tex]\[ V = \frac{175}{3} \][/tex]
When you divide 175 by 3, you get:
[tex]\[ V = 58 \frac{1}{3} \, \text{cm}^3 \][/tex]
So, the volume of the pyramid is:
[tex]\[ 58 \frac{1}{3} \, \text{cm}^3 \][/tex]
The correct answer is:
[tex]\[ 58 \frac{1}{3} \, \text{cm}^3 \][/tex]
