Question

a real estate development company is planning to build a unique community center in the shape of a pyramid to serve as a landmark for a new residential area. the pyramid will have a square base with a side length of 30 meters. the height of the pyramid will be 20 meters. the development company needs to estimate the space available inside the pyramid for planning the layout of different amenities. calculate the volume of the pyramid using the formula for the volume ( v=\frac{1}{3}bh ). round the answer to the nearest whole number, if necessary. use the keypad to enter the answer in the box. ( v=square m^{3} )

Explanation:

Step1: Calculate the area of the base \( B \)

The base is a square with side length \( s = 30\) meters. The area of a square is \( B=s^{2}\). So, \( B = 30\times30=900\) \(m^{2}\).

Step2: Substitute \( B \) and \( h \) into the volume formula

The formula for the volume of a pyramid is \( V=\frac{1}{3}Bh\), where \( h = 20\) meters. Substitute \( B = 900\) and \( h=20\) into the formula: \( V=\frac{1}{3}\times900\times20\).
First, calculate \( 900\times20 = 18000\). Then, \( V=\frac{18000}{3}\).

Step3: Simplify the expression

\( V = 6000\) \(m^{3}\).

Answer:

\(6000\)