Question

this square - based oblique pyramid has a volume of $125\\ m^3$. what is the height of the pyramid? $\square$ m

Explanation:

Step1: Recall the volume formula for a pyramid

The volume \( V \) of a pyramid is given by the formula \( V=\frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height.

Step2: Calculate the area of the square base

The base is a square with side length \( s = 5\space m \). The area of a square is \( B=s^2 \), so \( B = 5^2=25\space m^2 \).

Step3: Substitute the known values into the volume formula and solve for \( h \)

We know that \( V = 125\space m^3 \) and \( B = 25\space m^2 \). Substituting into \( V=\frac{1}{3}Bh \), we get \( 125=\frac{1}{3}\times25\times h \). First, simplify the right - hand side: \( \frac{1}{3}\times25\times h=\frac{25h}{3} \). Then, solve for \( h \) by multiplying both sides of the equation by \( 3 \): \( 125\times3 = 25h \), which gives \( 375 = 25h \). Then divide both sides by \( 25 \): \( h=\frac{375}{25}=15 \).

Answer:

\( 15 \)