Question

a hotel is in the shape of a square pyramid. each side of the base is 183 meters long and the height is 110 meters. what is the hotels volume? enter your answer in the box

Explanation:

Step1: Calculate the area of the base

The base is a square with side length \(a = 183\) m. The area of a square \(B=a^{2}\), so \(B = 183^{2}=183\times183 = 33489\space m^{2}\)

Step2: Use the volume formula for a pyramid

The volume formula for a pyramid is \(V=\frac{1}{3}Bh\), where \(B\) is the area of the base and \(h\) is the height. Given \(h = 110\) m and \(B=33489\space m^{2}\)

Substitute the values into the formula: \(V=\frac{1}{3}\times33489\times110\)

First, \(\frac{1}{3}\times33489 = 11163\)

Then, \(11163\times110=1227930\space m^{3}\)

Answer:

\(1227930\)