It is known that the area of the largest equilateral triangular
section of a cube is 140sq cm. What is the side length of the cube?
The distances between the centres of two adjacent faces of another
cube is 8cms. What is the side length of this cube? Another cube
has an edge length of 12cm. At each vertex a tetrahedron with three
mutually perpendicular edges of length 4cm is sliced away. What is
the surface area and volume of the remaining solid?
This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the triangle.
A spider is sitting in the middle of one of the smallest walls in a
room and a fly is resting beside the window. What is the shortest
distance the spider would have to crawl to catch the fly?
If the sector is made into a cone by closing up the gap, what
will be the base radius for that cone?
If the cone now suffers a horizontal cut which removes the top
and reduces the height of what remains to half the original cone
height, what curved surface area does that lower shape now
Can you see that an apple can be approximated to a stack of
"headless cones" ?
Not very tall ones!
And you could use that curved surface area calculation you did
earlier to get an approximation for the total apple peel.
Maybe use a spreadsheet to get improved accuracy with more
frustums (the name for headless cones!) ?