3 Vocabulary Terms - Define/Illustrate
1. Difference between a Cylinder and a Cone:
2. When to use Pythagorean Theorem and when to use volume? 3. Examples of Cones in real-life:
1.
Cylinder: A cylinder is a three-dimensional shape with two parallel circular bases of the same size, connected by a curved surface. The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius of the base and h is the height of the cylinder.
Cone: A cone is a three-dimensional shape with a circular base and a curved surface that tapers to a point called the apex. The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.
Illustration: In the illustration, the cylinder and cone are shown side by side, highlighting the differences in their shapes and structures. The cylinder has two circular bases of equal size, while the cone has a single circular base that tapers to a point at the apex.
2.
Pythagorean Theorem: The Pythagorean Theorem is used to calculate the lengths of the sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The formula is a^2 + b^2 = c^2, where a and b are the lengths of the two shorter sides, and c is the length of the hypotenuse.
Volume: Volume is the amount of space occupied by a three-dimensional object. It is commonly calculated by multiplying the area of the base by the height of the object. The formula for calculating the volume of simple shapes such as cubes, cylinders, and cones is often used in geometry.
In general, the Pythagorean Theorem is used to find missing side lengths in a right triangle, while the volume formula is used to find the amount of space an object occupies in three dimensions.
3.
Examples of cones in real life:
- Traffic cones: Traffic cones are commonly used on roads to redirect traffic and indicate construction zones. They have a cone shape with a wide base and narrow apex.
- Ice cream cones: Ice cream cones are often used to hold scoops of ice cream. They have a conical shape that tapers to a point at the top.
- Pinecones: Pinecones are seed-bearing cones that are found on pine trees. They have a conical shape and protective scales that open to release seeds.