math: find the area of a circle

Math: Find the area of a circle.

Science: Describe the impact of catastrophic events on the Earth (Earthquake)

By Alfonso Salinas, Oralia Fernandez and Diana De Alba.

Pre-requisites: Math and Science

• Circumference (radius, chord, diameter, arch)

• Concept of Area • Coordinate Plane

• Rates

• Tectonic Plates

Activity to discover “Area of a circle”Organize class into groups.

Distribute:

a) Template of a Circleb) Rulerc) Scissors

E x p l o r e ! Step 1. Students are to sketch 6 more diameters on the given template of a circle.

Step 2. Students are to cut out the circle through one of the diameters.

Step 3. Cut out the circle through all the radii towards the circumference

Step 4. Try to fit the pieces you have into a known polygon

How does it looks like?

How does it looks like?

Rectangle, parallelogram

What parts could you label in this figure?

What parts could you label in this figure?

Base or Length

Height or

Width

Develop the formula for the area of a circle based on the formula for the area of a rectangle or

parallelogram

Area of a Rectangle = Length x Width

A = L . W A = (½ C ) (radius)

A = (½ )2πr.r

A = 2πr.r

2

A = π r.r

A = πr2

This is the formula for the Area of a circle.

How does an Earthquake wave travel?

Observe the following animation

How fast red, yellow and blue lines travel ?

USGS Science for a changing world

http://neic.usgs.gov/neis/eq_depot/2002/eq_021103/ak_seismic_waves.html

Types of Earthquake Waves

Types of Earthquake Waves

AREA = 1,385.44 Km2

Source http://nemo.sciencecourseware.org/VirtualEarthquake/VQuakeExecute.html

r=21Km

If the average velocity of a P-Waves is

7 Km/Sec.

Find the area of seismic activity within

three seconds.

Types of Earthquake Waves

AREA = 706.86 Km2

Source http://nemo.sciencecourseware.org/VirtualEarthquake/VQuakeExecute.html

r=15Km

If the average velocity of a S-Waves is

5 Km/Sec. Find the area of seismic

activity within three seconds.

Types of Earthquake Waves

Earthquakes Effects

Let’s Analyze in the following Earthquake simulator The Earthquake effects.

Earthquakes Effects

What is the relationship for destruction compared to Increasing the magnitude of the movement in the Earthquake simulator ?

How does Mathematicians find some “centers”

The Centroid of a triangle is the point where the three medians of the triangle intersect.

How does Mathematicians find some “centers”

The Circumcenter The point where the three perpendicular bisectors of a triangle meet.

How does Mathematicians find some “centers”

The orthocenter of a triangle is the point where its altitudes intersect.

How does Mathematicians find some “centers”

The Incenter of the triangle is the point where the three angle bisectors of a triangle meet.

If dermis is the skin and epidermis is the outer layer of the skin. What do you think would be the meaning for “epi”?

EP/EPI comes from Greek and means variously “upon,” “besides,” “attached to,” “over,” “outer,” or “after.”

An epicenter is the portion of the earth’s surface directly over the focus of an earthquake.

How does scientists find and epicenter of an earthquake?

1. Calculate the S-P time for at least 3 seismograph recordings. The P-wave is the first wave spike, the S-wave is the much bigger wave spike just after the P wave.

2. Using these measurements to find the distance from the epicenter using a standardized P and S wave chart.

3. Use these the distance at each station to draw a circle of that radius around the station

4 After drawing at least 3 circles, the intersection of the circles is the epicentre.

How does scientists find and epicenter of an earthquake?

Find the area of seismic activity

for each seismograph.

A = πr2

Scale 1cm = 100 km

How does scientists find and epicenter of an earthquake?

Scale 1cm = 100 km