Geometry Answers

The total area of a regular tetrahedron is 110.85 m2, determine its base edge.

6. If the lateral area of a right circular cylinder is 90 cm2 and its volume is 225 cm3, find its radius.

7. Determine the lateral area of a cylinder of height 300mm and base radius of 100mm.

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.

Let BCB′C′ be a rectangle, let M be the midpoint of B′C′, and let A be a point on the circumcircle of the rectangle. Let triangle ABC have orthocenter H, and let T be the foot of the perpendicular from H to line AM. Suppose that AM= 2, [ABC] = 2020, and BC= 10. Then AT=m/n, where m and n are positive integers with gcd (m,n) = 1. Compute 100m+n.

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