circle circumference

Let us study about Circle Circumference,
The circumference of a circle is the actual length around the circle which is equal to 360°. Pi (p) is the number needed to compute the circumference of the circle.
p is equal to 3.14.
Pi is greek and has been around for over 2000 years!

In circles the AREA is equal to 3.14 (p) times the radius (r) to the power of 2.
Thus the formula looks like:
A= pr2.

In circles the circumference is 3.14 (p) times the Diameter.
Thus the formula looks like:
2pr or pd.

Example :

A circular swimming pool has a radius of 14 m. Find the circumference of the pool.

Solution:






So, the circumference of the pool is 88 m.

Note:


I hope the above explanation was useful.

Right Circular Cylinders

Let us study about Right Circular Cylinders,
A prism shaped solid whose bases are circles is a cylinder. If the segment joining the centers of the circles of a cylinder is perpendicular to the planes of the bases, the cylinder is a right circular cylinder. In Figure 1, cylinder (a) is a right circular cylinder and cylinder (b) is an oblique circular cylinder.

Figure 1 Different types of circular cylinders.

Lateral area, total area, and volume for right circular cylinders are found in the same way as they are for right prisms.

If a cylinder is pictured as a soup can, its lateral area is the area of the label. If the label is carefully peeled off, the label becomes a rectangle, as shown in Figure 2

Figure 2 The lateral area of a cylinder.

The area of the label is the area of a rectangle with a height the same as the altitude of the can and a base the same as the circumference of the lid of the can.

Theorem: The lateral area, LA, of a right circular cylinder with a base circumference C and an altitude h is given by the following equation.




Theorem: The total area, TA, of a right circular cylinder with lateral area LA and a base area B is given by the following equation.

Theorem: The volume of a right circular cylinder, V, with a base area B and altitude h is given by the following equation.

Example 1: Figure 3 is a right circular cylinder; find (a) LA (b) TA and (c) V.

Figure 3

Finding the lateral area, total area, and volume of a right circular cylinder.

Hope the above explanation helped you.

Congruent Triangles

We will learn about Congruent triangles,
Three noncolinear points determine a triangle. Draw the three segments connecting the three pairs of points and find three sides, and 3 interior angles, hence the name triangle.

Two triangles are congruent if one can be moved on top of the other, so that edges and vertices coincide. The corresponding sides have the same lengths, and corresponding angles are congruent.


Assume the edges of one triangle are the same lengths as the corresponding edges of another triangle. Move the first triangle onto the second so that the bases coincide. Do the apexes also coincide? Both apexes are x units away from the left end of the base, and y units from the right end of the base. Since the triangles are oriented the same way, both apexes lie above the base. Draw a circle of radius x centered at the left end of the base, and a circle of radius y centered at the right end of the base. These circles intersect in precisely two points, one above the base and one below. Thus there is only one possible location for the apex. Both apexes coincide, and the first triangle lies directly on top of the second. Corresponding angles coincide, and are congruent. This method of proving triangle congruence is called SSS, for side side side.

Hope the above explanation helped you, now let us study about types of triangles.