Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
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]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.