A right pyramid with a square base has a base length of x inches and a height of (x + 2) inches. The height is two inches longer than the base length. Which expression represents the volume in terms of x?
A) \( \frac{x^2 (x + 2)}{3} \) cubic inches
B) \( \frac{x (x + 2)}{3} \) cubic inches
C) \( \frac{x^3}{3} + 2 \) cubic inches
D) \( x^3 + 2 \)
Answer (1)
To find the expression that represents the volume of a right pyramid with a square base in terms of the base length x , we'll follow these steps:
Formula for the Volume of a Pyramid:
The formula to calculate the volume V of a pyramid is given by:
V = 3 1 × Base Area × Height
Determine the Base Area:
The base of the pyramid is a square with a side length of x . Therefore, the area of the base A is:
A = x 2
Define the Height:
The height of the pyramid is given as two inches longer than the side length of the base, which is x + 2 .
Substitute the Values into the Volume Formula:
Substitute the base area and height into the volume formula:
V = 3 1 × x 2 × ( x + 2 )
Simplifying, we have the expression for the volume:
V = 3 x 2 ( x + 2 )
Thus, the correct expression that represents the volume of the pyramid in terms of x is:
3 x 2 ( x + 2 ) cubic inches.
Therefore, the correct multiple-choice option is (A).
