Question

A pyramid has height x cm and a square base whose edges are 3 cm less than twice the height. Find the volume.

a) V = x^3 - 3x^2
b) V = x^3 - 9x
c) V = x^3 - 6x^2
d) V = x^3 - 3x

Answer 1

The volume of the pyramid is (2x^3 - 6x^2 + 9x - 9/3) cm^3, which simplifies to x^3 - 3x.

Step-by-step explanation:

The volume of a pyramid is given by the formula V = (1/3)Bh, where B is the area of the base and h is the height. In this case, the base is a square, so we can find the area using the formula B = s^2, where s is the length of the side of the square. Let's substitute the given information into the formula:

Base length = 2x - 3 cm

Area of base = (2x - 3)^2 cm^2

Volume of pyramid = (1/3)(2x - 3)^2(x) cm^3

Simplifying this expression, we get V = (2x^3 - 6x^2 + 9x - 9/3) cm^3

Thus, the correct answer is d) V = x^3 - 3x.