Question

A pyramid has a square base with sides of length s. The height of the pyramid is equal to of the length of a side on the base. Which formula represents the volume of the pyramid?

A.V=1/12s^3

B.V=1/6s^3

C.V=1/3s^3

D.V=3s^3

E.V=6s^3

Answer 1

Answer:²

V = (1/3)s³

Step-by-step explanation:

The area of a square base with side length s is A = s².  The volume of this pyramid is thus V = (1/3)s²h, where h represents the height.  We are told that the height is equal to s.  Thus, V = (1/3)s³.  This matches Answer C.

Note:  when possible answer choices are given to you, please share them.  Also, please enclose fractions inside parentheses to eliminate ambiguity.

Answer 2

The volume of the pyramid with a base area of s² and the height s is $\frac{1}{3} s^3$

The formula for calculating the volume of a square based pyramid is expressed as:

Volume = 1/3 * Base area * Height

Since it is a square-based pyramid, the base area is calculated as:

Base Area = s²

If the height of the pyramid is equal to of the length of a side on the base, hence h = s

Substituting the base area and the height into the formula for the volume, this will give;

$V = BH/3\\V = \frac{s^2\times s}{3} \\V =\frac{s^3}{3}\\V=\frac{1}{3} s^3$

Hence the volume of the pyramid with a base area of s² and the height s is $\frac{1}{3} s^3$

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