# Tag Archives: cubes

## Non-Congruent Triangles

Among the triangles of the previous problem (repeated below), how many distinct (non-congruent) triangles exist? Previous Problem: How many distinct triangles can be constructed by choosing three vertices from among the corners of a unit cube? Source: NCTM Mathematics Teacher, … Continue reading

## Distinct Triangles

How many distinct triangles can be constructed by choosing three vertices from among the corners of a unit cube? Source: NCTM Mathematics Teacher, February 2008 Solution We construct four triangles from three corners of a face for a total of … Continue reading

## Ball and Cube

Suppose that the volume of a ball is equal to times the volume of a cube. What is the ratio of the surface area of the ball to that of the cube? Source: NCTM Mathematics Teacher, September 2006 Solution Let … Continue reading

## Volumes of Two Cubes

The combined volumes of two cubes with integer side lengths are numerically equal to the combined lengths of their edges. What are the dimensions of the cubes? Source: NCTM Mathematics Teacher, January 2006 Solution Suppose is the side length of … Continue reading

## Corners of a Cube

All corners were sliced off a cube whose volume was cubic centimeters. Triangular faces are located where the cube’s vertices were. Each triangle is equilateral with -centimeter sides. Determine the total numbers of edges on the new solid. Source: NCTM … Continue reading

## Measure of Angle

, and are vertices of a cube, as shown. Find the measure of . Source: NCTM Mathematics Teacher, December 2005 SOLUTION Triangle is equilateral because its three sides are diagonals of a square. The measure of equals . Answer:

## Tetrahedron

Four of the nonadjacent vertices of a cube form a regular tetrahedron. What is the ratio of the surface area of the cube to the surface area of the tetrahedron? Source: NCTM Mathematics Teacher, December 2005 SOLUTION Let the side … Continue reading

## Red Face

A cube with all its faces painted red is cut into cubes that are . Some of these new cubes will have some red faces. The cubes are placed in a bag and thoroughly mixed. One is drawn at random … Continue reading

## Sphere and Cube

A sphere of radius and a cube of edge length have the same total surface area. Find in terms of . Source: NCMT Mathematics Teacher, February 2006 SOLUTION Surface area of sphere = Surface area of cube = Answer: square … Continue reading

## Octahedron

Consider a cube of side . The centers of each pair of faces of the cube sharing a common edge are connected to form a regular octahedron (a regular polyhedron with equilateral triangular faces). What is the volume of this … Continue reading