Geometry Answers

The surface area of a sphere inscribed in a regular tetrahedron is 144pi cm^2.
1. What is the radius of the sphere?

2. What is the altitude of the tetrahedron?

The surface area of a sphere inscribed in a regular tetrahedron is 144 cm2

What is the radius of the sphere?

Median AM and height BH triangle ABC (H - on the side AC) intersect at the point P. Find PH, if a AM = BH = 196, MN = 61, Where N - continuation intersection point AM with a circle around a triangle ABC. In response, write down the sum of possible values PH.

Let be H - the point of intersection of the heights of an acute-angled triangle ABC. From points A and C drawn tangents AK and CT to the circle drawn on the line segment BH as in diameter. Let be 15 and 17 - the lengths of these tangents. What is the smallest possible side length AC? In response, write down the square of the length AC.

At the base of the triangular pyramid DABC lies an isosceles acute-angled triangle ABC (AC = BC). It is known that CB > AD, and the edge DA is perpendicular to the plane ABC. The projections of the pyramid are considered DABC on the planes containing the straight line AC. It is known that the largest area of such a projection is 37, the smallest is 12, and the area of the triangle ABC is 35. Find the volume of the pyramid DABC. In response, write down the square of the volume.

The surface area of a sphere inscribed in a regular tetrahedron is 144 cm2

23. If a sphere is inscribed in a cube of side What is the volume of the sphere?


a) 36πcm^3

b) 8/3πcm^3

c) 288πcm^3

d) 972πcm^3

The surface area of a sphere inscribed in a regular tetrahedron is 144 cm2

22. What is the altitude of the tetrahedron?.


a) 20 cm

b) 24 cm

c) 28 cm

d) 48 cm

The surface area of a sphere inscribed in a regular tetrahedron is 144 cm2

21. What is the radius of the sphere?


a) 12 cm

b) 7 cm

c) 6 cm

d) 5 cm

17. A rectangular solid whose dimensions are 4cm, 8cm, and 12cm is inscribed in a sphere. What is the diagonal of the rectangular solid?


a) 7.49 cm

b) 8.94 cm

c) 14.42 cm

d) 14.97 cm

16. Identify a polyhedron with two congruent bases that lie in parallel planes, and whose every section that is parallel to a base has the same area as that of the base.


a) Prism

b) Pyramid

c) Circular Cylinder

d) Right Circular Cone