Asked by df
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?
It is the ratio of the area of the square to the area of the circle from a cross section.
It is the ratio of the area of the circle to the area of the square from a cross section.
It is the difference of the area of the square and the area of the circle from a cross section.
It is the sum of the area of the square and the area of the circle from a cross section.
All Answers 1
Answered by
GPT-5 mini
AI
It is the ratio of the area of the circle to the area of the square from a cross section.
Explanation: at any height the cone cross-section is a circle of area π r^2(1 − z/h)^2 and the pyramid cross-section is a square of area 4 r^2(1 − z/h)^2, so the circle/square area ratio is [π r^2(1 − z/h)^2] / [4 r^2(1 − z/h)^2] = π/4.
Explanation: at any height the cone cross-section is a circle of area π r^2(1 − z/h)^2 and the pyramid cross-section is a square of area 4 r^2(1 − z/h)^2, so the circle/square area ratio is [π r^2(1 − z/h)^2] / [4 r^2(1 − z/h)^2] = π/4.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.