Chapter 11.3, Problem 36PPS

(a)

To determine

To Find: The ratio of perimeter of pyramid of the sun to the great pyramid.

Answer to Problem 36PPS

  $0.97$

Explanation of Solution

Given: The perimeter of the base of the pyramid of the sun is $4\pi$ times the height. The perimeter of base of the great pyramid of Giza is $2\pi$ times the height.

  

Let $h_1$ be the height of the pyramid of sun and $h_2$ be the height of great pyramid.

Then

We have to find the ratio of perimeter of pyramid of the sun to the great pyramid

Perimeter of pyramid of sun = $4\pi h_1$

Perimeter of great pyramid of Giza= $2\pi h_2$

Then

Ratio is

  $\begin{array}{l}\frac{4\pi h_1}{2\pi h_2}=\frac{2h_1}{h_2}\\ h_1=233.5\\ h_2=481.4\\ \frac{2h_1}{h_2}=\frac{2(233.5)}{481.4}=0.97\end{array}$

Hence the ratio is $0.97$

(b)

To determine

To Find: The ratio of perimeter of the great pyramid to pyramid of the sun.

Answer to Problem 36PPS

  $1.03$

Explanation of Solution

Given: The perimeter of the base of the pyramid of the sun is $4\pi$ times the height. The perimeter of base of the great pyramid of Giza is $2\pi$ times the height.

  

Let $h_1$ be the height of the pyramid of sun and $h_2$ be the height of great pyramid.

Then

We have to find the ratio of perimeter of pyramid of the sun to the great pyramid

Perimeter of pyramid of sun = $4\pi h_1$

Perimeter of great pyramid of Giza= $2\pi h_2$

Then

Ratio is

  $\begin{array}{l}\frac{2\pi h_2}{4\pi h_1}=\frac{h_2}{2h_1}\\ h_1=233.5\\ h_2=481.4\\ \frac{2h_1}{h_2}=\frac{481.4}{2(233.5)}=1.03\end{array}$

Hence the ratio is $1.03$