The Oblique Pyramid Has A Square Base With An Edge Length Of 5 Cm. The Height Of The Pyramid Is 7 Cm.What Is The Volume Of The Pyramid?A. ${ 11 \frac{2}{3} \text{ Cm}^3\$} B. ${ 43 \frac{3}{4} \text{ Cm}^3\$} C. [$58 \frac{1}{3}
Introduction
In geometry, a pyramid is a three-dimensional shape with a square or polygonal base and triangular faces that meet at the apex. The oblique pyramid is a type of pyramid where the apex is not directly above the center of the base. In this article, we will explore how to calculate the volume of an oblique pyramid with a square base.
Understanding the Formula
The volume of a pyramid is given by the formula:
V = (1/3) * B * h
where V is the volume, B is the area of the base, and h is the height of the pyramid.
Calculating the Volume of the Oblique Pyramid
Given that the oblique pyramid has a square base with an edge length of 5 cm and a height of 7 cm, we can calculate its volume using the formula.
First, we need to find the area of the base. Since the base is a square, the area is given by:
B = s^2
where s is the edge length of the square.
In this case, the edge length is 5 cm, so the area of the base is:
B = 5^2 = 25 cm^2
Now, we can plug in the values into the formula to calculate the volume:
V = (1/3) * 25 * 7
V = (1/3) * 175
V = 58.33 cm^3
Converting the Volume to a Mixed Number
To convert the decimal volume to a mixed number, we can divide the decimal part by the denominator (3) and round to the nearest whole number.
58.33 ÷ 3 = 19.44 (round to 19)
So, the volume of the oblique pyramid is:
V = 58 1/3 cm^3
Conclusion
In this article, we calculated the volume of an oblique pyramid with a square base using the formula V = (1/3) * B * h. We found that the volume of the pyramid is 58 1/3 cm^3. This calculation demonstrates the importance of understanding geometric formulas and how to apply them to real-world problems.
Discussion
Which of the following options is the correct answer for the volume of the oblique pyramid?
A. ${11 \frac{2}{3} \text{ cm}^3\$} B. ${43 \frac{3}{4} \text{ cm}^3\$} C. ${58 \frac{1}{3} \text{ cm}^3\$}
Answer
The correct answer is C. ${58 \frac{1}{3} \text{ cm}^3\$}
Additional Resources
For more information on geometry and calculating volumes, check out the following resources:
Related Topics
- Calculating the Volume of a Cube
- Understanding Geometric Formulas
- Real-World Applications of Geometry
The Oblique Pyramid: Q&A ==========================
Introduction
In our previous article, we explored how to calculate the volume of an oblique pyramid with a square base. In this article, we will answer some frequently asked questions about the oblique pyramid and provide additional information to help you better understand this geometric shape.
Q: What is an oblique pyramid?
A: An oblique pyramid is a type of pyramid where the apex is not directly above the center of the base. This means that the pyramid is not a perfect pyramid, but rather a more complex shape with a square or polygonal base and triangular faces that meet at the apex.
Q: What is the formula for calculating the volume of an oblique pyramid?
A: The formula for calculating the volume of an oblique pyramid is:
V = (1/3) * B * h
where V is the volume, B is the area of the base, and h is the height of the pyramid.
Q: How do I calculate the area of the base of an oblique pyramid?
A: To calculate the area of the base of an oblique pyramid, you need to know the edge length of the square or polygonal base. The area of the base is given by:
B = s^2
where s is the edge length of the square or polygon.
Q: What is the difference between an oblique pyramid and a perfect pyramid?
A: The main difference between an oblique pyramid and a perfect pyramid is that the apex of an oblique pyramid is not directly above the center of the base, while the apex of a perfect pyramid is directly above the center of the base. This means that an oblique pyramid has a more complex shape than a perfect pyramid.
Q: Can I use the same formula to calculate the volume of a perfect pyramid?
A: Yes, you can use the same formula to calculate the volume of a perfect pyramid. The formula V = (1/3) * B * h is applicable to both oblique pyramids and perfect pyramids.
Q: What are some real-world applications of the oblique pyramid?
A: The oblique pyramid has several real-world applications, including:
- Architecture: Oblique pyramids are used in the design of buildings and monuments.
- Engineering: Oblique pyramids are used in the design of bridges and other structures.
- Art: Oblique pyramids are used in the creation of sculptures and other art forms.
Q: Can I use a calculator to calculate the volume of an oblique pyramid?
A: Yes, you can use a calculator to calculate the volume of an oblique pyramid. Simply plug in the values for the area of the base and the height of the pyramid, and the calculator will give you the volume.
Q: What are some common mistakes to avoid when calculating the volume of an oblique pyramid?
A: Some common mistakes to avoid when calculating the volume of an oblique pyramid include:
- Forgetting to square the edge length of the base.
- Forgetting to multiply the area of the base by the height.
- Using the wrong formula for the volume of a pyramid.
Conclusion
In this article, we answered some frequently asked questions about the oblique pyramid and provided additional information to help you better understand this geometric shape. We hope that this article has been helpful in clarifying any confusion you may have had about the oblique pyramid.
Additional Resources
For more information on geometry and calculating volumes, check out the following resources: