There's No Place Like Home
In this module, students will examine several types of structures, the geometric shapes that represent them, and the properties that help make buildings efficient. Some examples of dwellings we will be discussing can be seen here.
Definitions and Examples.
Inscribed polygon - A polygon in which each vertex of the polygon lies on a circle. Examples.
Radius of a regular polygon - The radius of the circle in which the polygon can be inscribed. Examples.
Tangent to a circle - A line, segment, or ray that intersects a circle in one point and is perpendicular to a radius at that point. Examples.
Right prism - A prism which has bases aligned one directly above the other and has lateral faces that are rectangles. Examples.
Volume of a right prism - The amount of space occupied by an object. The volume of a prism may be found by multiplying the area of its bases (B) by the height (h): V=Bh.
Volume of a cylinder - Found by multiplying the area of the base by the height. Examples.
Arc of a circle - The part of the circle whose endpoints are the intersections, with the circle, of the sides of a central angle. Examples.
Measure of an arc - The measure of its central angle. Examples.
Minor arc - An arc that has a measure less than 180°.
Major arc - An arc that has a measure greater than 180°.
Semicircle - An arc that measures exactly 180°.
Examples of major and minor arcs.
Length of an arc - The distance on the circle between the arc's endpoints. The distance can be found by multiplying the circle's circumference by the fractional part of the circle that the arc represents. Examples.
Sector of a circle - A region that is bounded by the sides of a central angle and an arc of the circle. The area can be found by multiplying the circle's area by the fractional part of the circle that the sector represents. Examples. More examples.
More examples of arc length and area of a sector.
Lateral surface area of a cone - The sector of a circle.
Total surface area of a cone - The sector of a circle added to the area of the base. Examples. More examples.
Examples of finding surface area of spheres, cones, cylinders, and pyramids.
Volume of a cone. Practice finding the volume of a cone.
Example of deriving the formula for the volume of a cone.
More examples of finding surface area and volume of geometric shapes.