Question

question 1 - 27
a tent in the shape of a square pyramid has a volume of 6.25 cubic meters. the height of the tent is 3 meters. what is the edge length of the base of the tent? enter the answer in the box as a decimal

m

Explanation:

Step1: Recall the volume formula for a square pyramid

The volume \( V \) of a square pyramid is given by the formula \( V=\frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height of the pyramid. Since the base is a square, if the edge length of the base is \( s \), then the area of the base \( B = s^{2}\). So the volume formula becomes \( V=\frac{1}{3}s^{2}h \).

Step2: Substitute the given values into the formula

We know that \( V = 6.25 \) cubic meters and \( h=3 \) meters. Substituting these values into the formula \( 6.25=\frac{1}{3}\times s^{2}\times3 \).

Step3: Simplify the equation

Simplify the right - hand side of the equation: \( \frac{1}{3}\times3\times s^{2}=s^{2} \). So our equation becomes \( s^{2}=6.25 \).

Step4: Solve for \( s \)

To find \( s \), we take the square root of both sides of the equation \( s = \sqrt{6.25} \). Since \( 2.5\times2.5 = 6.25 \), we have \( s = 2.5 \).

Answer:

\( 2.5 \)