Question

someone please help me, im so confused ack. In the derivation of the formula for the volume of a cone, the volume of the cone is calculated to be StartFraction pi Over 4 EndFraction times the volume of the pyramid that it fits inside. A cone is inside of a pyramid with a square base. The cone has a height of h and a radius r. The pyramid has a base edge length of 2 r. Which statement best describes where the StartFraction pi Over 4 EndFraction comes from in the formula derivation? A. It is the ratio of the area of the square to the area of the circle from a cross section. B. It is the ratio of the area of the circle to the area of the square from a cross section. C. It is the difference of the area of the square and the area of the circle from a cross section. D. It is the sum of the area of the square and the area of the circle from a cross section.

Answer 1

b

Explanation:

Answer 2

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.

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;

`((1)/(3) * \pi * r^2* h)/((1)/(3) *( 2 * r)^2* h)`

Given that the height are equal, h/h = 1, which gives;

`((1)/(3) * \pi * r^2)/((1)/(3) *( 2 * r)^2) = (Area \ of \ the \ circle)/(Area \ of \ the \ square) =((1)/(3) * \pi * r^2)/((1)/(3) * 4 * r^2) = (\pi )/(4)`

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.