The side of the base of the regular quadrangular pyramid is 14 dm and the height is 24 dm.

| April 25, 2021 | education

The side of the base of the regular quadrangular pyramid is 14 dm and the height is 24 dm. Find the volume of the cone inscribed in the pyramid.

To find the volume of the cone, use the formula:
V к = 1/3 * π * r² * h.
The height of the cone is equal to the height of the pyramid, the radius is half the side of the base (at the base is a square).
V к = 1/3 * π * 7² * 24 = 392π (dm³).
Another solution is possible.
We find the volume of this pyramid:
V p = 1/3 * S * h = 1/3 * 14² * 24 = 1568 (dm³).
For a regular quadrangular pyramid, the ratio of the volume of an inscribed cone to the volume of a regular pyramid is:
Vк / Vп = π / 4, from which it follows:
Vк = Vп * π / 4 = 1568 * π / 4 = 392π (dm³).
Answer: the volume of the inscribed cone is 392π dm³.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.