Think back to the spider problem. We opened our box ( a rectangular prism) to find the shortest distance from the spider to the fly. The area taken up by that net doesn't depend on which net we use. The area of that net is the surface area of the box.
Nets of cubes
Volume of cubes: multiplication models
Prisms: parallel and congruent bases
building cubes from pyramids activity
volume of pyramids
Some notes before we start considering surface area of spheres:
- A tangent to a circle is a line that touches the circle at exactly one point.
- A tangent to a circle is always perpendicular to the radius that touches the point of tangency (place where the tangent line touches the circle.)
- Similar triangles have the same shape, but different sizes: all of our families of right triangles are similar. This means that the angles will be congruent (equal) and ratios of the sides are the same. (The sides are not the same, but they have the same ratio within and between the triangles as we have seen with our right triangle families.)
- We will watch just the cylinder explanation (11:30)