Question

the great pyramid of giza in egypt is one of the most famous pyramids in the world. egypt is also home to many more pyramids that are studied and visited today. the table below shows the planned dimensions of some of these square pyramids. order the volumes of the pyramids given in the table from least to greatest. what is the range in the volumes of the pyramids given in the table? round your answer to the nearest whole number. cubic meters

Explanation:

Step1: Calculate the volume of each pyramid

The volume formula for a square - pyramid is \(V=\frac{1}{3}s^{2}h\), where \(s\) is the base side length and \(h\) is the height.

• For the Red Pyramid: \(s = 220\) m, \(h=105\) m.

\(V_{1}=\frac{1}{3}\times220^{2}\times105=\frac{1}{3}\times48400\times105 = 48400\times35=1694000\) \(m^{3}\)

• For the Pyramid of Khafre: \(s = 215.25\) m, \(h = 143.5\) m.

\(V_{2}=\frac{1}{3}\times(215.25)^{2}\times143.5=\frac{1}{3}\times46331.0625\times143.5\approx\frac{1}{3}\times6658507.469\approx2219502.49\) \(m^{3}\)

• For the Pyramid of Menkaure: \(s = 103.4\) m, \(h = 65.5\) m.

\(V_{3}=\frac{1}{3}\times(103.4)^{2}\times65.5=\frac{1}{3}\times10691.56\times65.5\approx\frac{1}{3}\times699297.18\approx233099.06\) \(m^{3}\)

• For the Pyramid of Neferirkare: \(s = 105\) m, \(h = 72\) m.

\(V_{4}=\frac{1}{3}\times105^{2}\times72=\frac{1}{3}\times11025\times72 = 11025\times24 = 264600\) \(m^{3}\)

Step2: Order the volumes from least to greatest

Compare the values: \(V_{3}\approx233099.06\), \(V_{4} = 264600\), \(V_{1}=1694000\), \(V_{2}\approx2219502.49\)
The order is Pyramid of Menkaure, Pyramid of Neferirkare, Red Pyramid, Pyramid of Khafre.

Step3: Calculate the range

The range formula is \(R=\text{Max}-\text{Min}\).
The maximum volume is \(V_{2}\approx2219502.49\) \(m^{3}\), and the minimum volume is \(V_{3}\approx233099.06\) \(m^{3}\)
\(R=2219502.49 - 233099.06=1986403.43\approx1986403\) \(m^{3}\)

Answer:

The order from least to greatest: Pyramid of Menkaure, Pyramid of Neferirkare, Red Pyramid, Pyramid of Khafre.
The range is \(1986403\) cubic meters.