Answer:
The correct option is;
B. It is the ratio of the area of the circle to the area of the square from a cross section.
Step-by-step explanation:
The formula for the volume of a pyramid = 1/3*Area of base*Height
The formula for the volume of a cone = 1/3*Area of base*Height
The area of the base of the square pyramid of side 2r = 2r*2r = 4r²
The area of the base of the cone of base radius r = πr²
The ratio of the volume of the cone to the volume of the square pyramid is given as follows;
[tex]\dfrac{\dfrac{1}{3} \times \pi \times r^2\times h}{\dfrac{1}{3} \times( 2 \times r)^2\times h}[/tex]
Given that the height are equal, h/h = 1, which gives;
[tex]\dfrac{\dfrac{1}{3} \times \pi \times r^2}{\dfrac{1}{3} \times( 2 \times r)^2} = \dfrac{Area \ of \ the \ circle}{Area \ of \ the \ square} =\dfrac{\dfrac{1}{3} \times \pi \times r^2}{\dfrac{1}{3} \times 4 \times r^2} = \dfrac{\pi }{4}[/tex]
Therefore, where the π/4 comes from is that it is the ratio of the area of the circle to the area of the square from a cross section.
