# Geometry Tutor

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## Geometry Terms

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Below are some terms you will need to know in order to begin your study of geometry:

Points
- Points are used to specify exact locations.

Line Segment
- Distance between two points.

Planes
- A plane can be thought of as a two-dimensional flat surface, having length and width, but no height

Space
- Space is the set of all possible points on an infinite number of planes. Thus, space covers all three dimensions – length, width, and height.

Acute Angle
- An angle less than 90 degrees but greater than 0 degrees.

Right Angle
- A 90 degree angle.

Obtuse Angle
- An angle greater than 90 degrees but less than 180 degrees.

Vertex
- The intersection point of two sides of a plane figure.

- A straight line extending from the center of a circle or sphere to the circumference or surface.

## Geometry Word Problems

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## Solved Examples

Question 1: Find the area of the circular ring having radius 12 cm.
Solution:
Step 1:
Radius of circle = 12 cm
Area of the circle = ?

Step 2:

Area of the circle = $\pi r^2$

= $\frac{22}{7}$ (12)2

= $\frac{22}{7}$ * 12 * 12

= $\frac{22}{7}$ * 144

= 452.6

Hence the area of the circle is 452.6 cm2 .

Question 2: Find the volume of the cylinder having radius 5 inches and height 8 inches.

Solution:
Step 1:
Radius of the cylinder (r) = 5 cm
Height of the cylinder (h) = 8 cm

Step 2:

Volume of a cylinder (V) =  $\pi$ r2 h

= $\frac{22}{7}$ * 52 * 6

= $\frac{22}{7}$ * 5 * 5 * 6

= $\frac{22}{7}$ * 150

= 471.42

Hence the volume of a cylinder is 471.42 inches3 .

Question 3: Find the surface area of a sphere of diameter 12 cm.(using $\pi$ = $\frac{22}{7}$)

Solution:
Step 1:
Diameter of a sphere (d) = 12 cm
Therefore radius of a sphere (r) = $\frac{d}{2} = \frac{12}{2}$ = 6 cm

Step 2:

Surface area of a sphere(SA) = 4 $\pi r^2$

= 4 *  $\frac{22}{7}$ *  $6^2$

= 4 * $\frac{22}{7}$ * 6 * 6

= 4 * $\frac{22}{7}$ * 36

= 452.57

Hence surface area of a sphere is 452.57 cm2.