Create ways to teach surface area and volume to students. (Real-Life Example)

Creating ways to teach surface area and volume. I am especially interested in methods which will help students connect geometry to life in the real world.

Find a creative way, using real-life examples, to teach surface area and volume.

Brainstorm creative ways to teach surface area and volume. The teachers are especially interested in methods which will help the students connect geometry to life in the real world because student motivation has sometimes been lacking in this course.

Differentiable geometry (tangent bundle, orientations)

Prove that the tangent bundle TM of a differentiable manifold M is (always) orientable (even though M may not be).

Differential Geometry : Projective Space, Orientations

Prove that the real projective space P^n(R) is orientable if and only if n is odd.

Geometry / Construction : Construct triangle ABC given just 3 points ,namely S= its circumcenter, H = its orthocenter and F = the foot of one of its alititudes.

Construct triangle ABC given just 3 points ,namely S= its circumcenter, H = its orthocenter and F = the foot of one of its alititudes.

Geometry : How many distinct points does the 9-point circle have when the triangle is isosceles, equilateral, right-angle isosceles

How many distinct points does the 9-point circle have when the triangle is - isosceles - equlateral - right-angled isosceles.

Geometry Applications

Geometry has many practical applications in everyday life. Estimating heights of objects, finding distances, and calculating areas and volumes are commonplace. One of the most fundamental theorems in geometry, the Pythagorean Theorem, allows us to make many of these calculations. The Pythagorean Theorem states that the square of ...continues

Geometry

(See attached file for full problem description with proper symbols) The area A of an equilateral triangle varies directly as the square of the length of a side. If the area if the equilateral triangle whose sides are of length 1 cm is (  3 ) / 4 cm 2 , find the length s of an equilateral triangle whose area A is ...continues

Finding the cubic yard

An engineer's plan shows a canal with a trapezoidal cross section that is 8 ft deep and 14 ft across at the bottom with walls sloping outward at an angle of 45 degrees. The canal is 620 ft long. A contractor bidding for the job estimates the cost to excavate the canal at $1.75 per cu yd. If the contractor adds 10% profit, what s ...continues

Differential Geometry, imbedded submanifold.

Let phi : R^2 --> R be a function given by phi(x,y) = x^3 + xy + y^3 +1 For which points p =(0,0) , p=(1/3,1/3), p =(-1/3,-1/3) is the subset phi^-1 ( phi(p)) an imbedded sub-manifold of R^2. ( This question was given as part of Differential Geometry course, we use Do Carmo's book,Riemannian Geometry) Please ...continues