The base edge of an oblique square pyramid is represented as $x cm$. If the height is 9 cm, what is the volume of the pyramid in terms of $x$?
A. $3 x^2 cm^3$
B. $9 x^2 cm^3$
C. $3 x cm^3$
D. $x cm^3$
Answer (1)
The problem provides the base edge ( x ) and height (9 cm) of an oblique square pyramid.
The area of the square base is calculated as B = x 2 .
The volume of the pyramid is found using the formula V = 3 1 B h .
Substituting the values, the volume is simplified to 3 x 2 c m 3 .
Explanation
Problem Analysis Let's analyze the problem. We are given an oblique square pyramid with a base edge of x cm and a height of 9 cm. We need to find the volume of the pyramid in terms of x .
Volume Formula The volume of a pyramid is given by the formula: V = 3 1 B h where B is the area of the base and h is the height.
Base Area Since the base is a square with side length x , the area of the base is: B = x 2
Substitute Values Now, substitute the base area B = x 2 and the height h = 9 into the volume formula: V = 3 1 ( x 2 ) ( 9 )
Simplify Simplify the expression: V = 3 9 x 2 V = 3 x 2 The volume of the pyramid is 3 x 2 cubic centimeters.
Final Answer Therefore, the volume of the oblique square pyramid in terms of x is 3 x 2 c m 3 .
Examples
Understanding the volume of a pyramid is useful in various real-world scenarios. For example, when designing structures like the Great Pyramid of Giza, engineers need to calculate the volume of the pyramid to estimate the amount of material required for construction. Knowing the base area and height, they can use the formula V = 3 1 B h to determine the volume and plan the construction accordingly. This principle applies to modern architecture as well, where pyramid-shaped structures are sometimes incorporated into building designs.
