Answer :
Sure, let's solve the problem step-by-step.
1. Identify the given values:
- The edge length of the square base of the pyramid is \(5 \, \text{cm}\).
- The height of the pyramid is \(7 \, \text{cm}\).
2. Calculate the area of the square base:
To find the area of the square base, we use the formula for the area of a square:
[tex]\[ \text{Base area} = \text{edge length}^2 \][/tex]
Substituting the given edge length:
[tex]\[ \text{Base area} = 5 \, \text{cm} \times 5 \, \text{cm} = 25 \, \text{cm}^2 \][/tex]
3. Calculate the volume of the pyramid:
The volume \(V\) of a pyramid is given by the formula:
[tex]\[ V = \frac{1}{3} \times \text{Base area} \times \text{height} \][/tex]
Using the values we have:
[tex]\[ V = \frac{1}{3} \times 25 \, \text{cm}^2 \times 7 \, \text{cm} = \frac{1}{3} \times 175 \, \text{cm}^3 = 58.\overline{3} \, \text{cm}^3 \][/tex]
4. Compare with the given multiple-choice options:
- \(11 \frac{2}{3} \, \text{cm}^3\)
- \(43 \frac{3}{4} \, \text{cm}^3\)
- \(58 \frac{1}{3} \, \text{cm}^3\)
- \(87 \frac{1}{2} \, \tex{Cl}^3\)
The calculated volume \(58.33333333333333 \, \text{cm}^3\) matches exactly with \(58 \frac{1}{3} \, \text{cm}^3\).
Therefore, the correct answer is:
[tex]\[ 58 \frac{1}{3} \, \text{cm}^3 \][/tex]
1. Identify the given values:
- The edge length of the square base of the pyramid is \(5 \, \text{cm}\).
- The height of the pyramid is \(7 \, \text{cm}\).
2. Calculate the area of the square base:
To find the area of the square base, we use the formula for the area of a square:
[tex]\[ \text{Base area} = \text{edge length}^2 \][/tex]
Substituting the given edge length:
[tex]\[ \text{Base area} = 5 \, \text{cm} \times 5 \, \text{cm} = 25 \, \text{cm}^2 \][/tex]
3. Calculate the volume of the pyramid:
The volume \(V\) of a pyramid is given by the formula:
[tex]\[ V = \frac{1}{3} \times \text{Base area} \times \text{height} \][/tex]
Using the values we have:
[tex]\[ V = \frac{1}{3} \times 25 \, \text{cm}^2 \times 7 \, \text{cm} = \frac{1}{3} \times 175 \, \text{cm}^3 = 58.\overline{3} \, \text{cm}^3 \][/tex]
4. Compare with the given multiple-choice options:
- \(11 \frac{2}{3} \, \text{cm}^3\)
- \(43 \frac{3}{4} \, \text{cm}^3\)
- \(58 \frac{1}{3} \, \text{cm}^3\)
- \(87 \frac{1}{2} \, \tex{Cl}^3\)
The calculated volume \(58.33333333333333 \, \text{cm}^3\) matches exactly with \(58 \frac{1}{3} \, \text{cm}^3\).
Therefore, the correct answer is:
[tex]\[ 58 \frac{1}{3} \, \text{cm}^3 \][/tex]
