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. $11 \frac{2}{3} cm^3$
B. $43 \frac{3}{4} cm^3$
C. $58 \frac{1}{3} cm^3$
D. $87 \frac{1}{2} cm^3
Answer (2)
Calculate the area of the square base: A = 5 2 = 25 cm 2 .
Apply the pyramid volume formula: V = 3 1 A h .
Substitute the values: V = 3 1 × 25 × 7 = 3 175 .
Determine the volume of the pyramid: 58 3 1 c m 3 .
Explanation
Problem Analysis We are given an oblique pyramid with a square base. The side length of the square base is 5 cm, and the height of the pyramid is 7 cm. Our goal is to find the volume of the pyramid.
Volume Formula The volume of a pyramid is given by the formula: V = 3 1 × A × h , where V is the volume, A is the area of the base, and h is the height of the pyramid. In our case, the base is a square with side length 5 cm, and the height is 7 cm.
Base Area Calculation First, we need to calculate the area of the square base. The area of a square is given by the formula: A = s 2 , where s is the side length of the square. In our case, s = 5 cm, so the area of the base is: A = 5 2 = 25 cm 2
Volume Calculation Now, we can calculate the volume of the pyramid using the formula: V = 3 1 × A × h . We have A = 25 cm 2 and h = 7 cm, so the volume is: V = 3 1 × 25 × 7 = 3 175 = 58 3 1 cm 3
Final Answer Therefore, the volume of the pyramid is 58 3 1 cm 3 .
Examples
Pyramids are not just ancient structures; they appear in modern architecture and even in food presentation! Imagine you're making a chocolate mousse dessert shaped like a pyramid. Knowing the volume calculation helps you determine how much mousse you need to fill each pyramid-shaped container. If your container has a square base of 6 cm and a height of 8 cm, the volume would be (1/3) * (6*6) * 8 = 96 cm³. This ensures you prepare the right amount of dessert, avoiding waste and creating perfectly portioned treats.
The volume of the oblique pyramid with a square base measuring 5 cm on each side and a height of 7 cm is calculated using the formula V = 3 1 A h , resulting in a volume of 58 3 1 c m 3 . Thus, the correct multiple-choice answer is C. 58 3 1 c m 3 .
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