Question

A pyramid has a square base with side s. The height of the pyramid is 2/3 that of its side. What is the expression for the volume of the pyramid?

Answer 1

Answer:

The required expression for the volume of pyramid is $V=\frac{2s^3}{9}$

Step-by-step explanation:

Consider the provided information.

A pyramid has a square base with side s. The height of the pyramid is 2/3 that of its side.

The volume of pyramid is: $V=\frac{lwh}{3}$

Where, l is base length, w is base width and h is the height.

It is given that the base is square therefore, l=s and w=s.

The height of pyramid is $\frac{2}{3}s$

Substitute the respective values in the above formula.

$V=\frac{s\times s\times \frac{2s}{3}}{3}$

$V=\frac{2s^3}{9}$

Hence, the required expression for the volume of pyramid is $V=\frac{2s^3}{9}$

Answer 2

I think the height is 2/3 that of a side of the base. If that is correct, then the height is h = 2/3s.

The formula for the volume of a pyramid is \[V=\frac{ 1 }{ 3 }s ^{2}h\]

Normally it would be B for base area, but since this is a square and the height is in terms of s, that would be the formula.

If we find the area based on the fact that h = 2/3s, then it appears that the formula would be

V=1/3s^2 x 2/3s

If you multiply that all out, it would be V= 2 / 9s ^3