Answer :
To find the volume of the pyramid, follow these steps:
1. Understand the formula for the volume of a pyramid:
The volume \( V \) of a pyramid can be calculated using the formula:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
2. Determine the shape and dimensions of the base:
In this case, the base of the pyramid is a square with an edge length of \( 5 \) cm.
3. Calculate the area of the square base:
The area \( A \) of a square is given by:
[tex]\[ A = \text{edge length}^2 \][/tex]
Substituting the given edge length:
[tex]\[ A = 5^2 = 25 \text{ cm}^2 \][/tex]
4. Use the height of the pyramid:
The given height \( h \) of the pyramid is \( 7 \) cm.
5. Apply the volume formula:
Substituting the base area \( A = 25 \text{ cm}^2 \) and the height \( h = 7 \text{ cm} \) into the volume formula:
[tex]\[ V = \frac{1}{3} \times 25 \text{ cm}^2 \times 7 \text{ cm} \][/tex]
Simplify the calculation:
[tex]\[ V = \frac{1}{3} \times 175 \text{ cm}^3 = 58.333\overline{3} \text{ cm}^3 \][/tex]
6. Match the calculation to the provided choices:
We convert the decimal \( 58.333\overline{3} \) to a fraction:
[tex]\[ 58.333\overline{3} = 58 \frac{1}{3} \][/tex]
Therefore, the volume of the pyramid is:
[tex]\[ 58 \frac{1}{3} \text{ cm}^3 \][/tex]
So, the correct answer is:
[tex]\[ 58 \frac{1}{3} \text{ cm}^3 \][/tex]
1. Understand the formula for the volume of a pyramid:
The volume \( V \) of a pyramid can be calculated using the formula:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
2. Determine the shape and dimensions of the base:
In this case, the base of the pyramid is a square with an edge length of \( 5 \) cm.
3. Calculate the area of the square base:
The area \( A \) of a square is given by:
[tex]\[ A = \text{edge length}^2 \][/tex]
Substituting the given edge length:
[tex]\[ A = 5^2 = 25 \text{ cm}^2 \][/tex]
4. Use the height of the pyramid:
The given height \( h \) of the pyramid is \( 7 \) cm.
5. Apply the volume formula:
Substituting the base area \( A = 25 \text{ cm}^2 \) and the height \( h = 7 \text{ cm} \) into the volume formula:
[tex]\[ V = \frac{1}{3} \times 25 \text{ cm}^2 \times 7 \text{ cm} \][/tex]
Simplify the calculation:
[tex]\[ V = \frac{1}{3} \times 175 \text{ cm}^3 = 58.333\overline{3} \text{ cm}^3 \][/tex]
6. Match the calculation to the provided choices:
We convert the decimal \( 58.333\overline{3} \) to a fraction:
[tex]\[ 58.333\overline{3} = 58 \frac{1}{3} \][/tex]
Therefore, the volume of the pyramid is:
[tex]\[ 58 \frac{1}{3} \text{ cm}^3 \][/tex]
So, the correct answer is:
[tex]\[ 58 \frac{1}{3} \text{ cm}^3 \][/tex]
