Surface Area of a Sphere

Today in Math Honours 10, we experimented with a real test of the surface area of a sphere. My partner for this experiment was Alhan, and we took apart an orange to show that the formula for the surface area of an orange is 4 $\pi$ $r^2$ .

We started by cutting our orange in half, and peeling it…

Next we traced the circumference of the oranges onto paper multiple times…

After that we carefully pulled the orange peels apart and placed them inside of the circles, one at a time, insuring that there was no white spaces and no overlapping.

Finally we came up with our formula 4 $\pi$ $r^2$ .

To estimate the volume of Garabaldi lake I’m going to multiply the average lake depth by the lake area.

119 m x 9940000

= 1 182 860 000  Metre’s Cubed or approximately 1 trillion litres.

The average lake depth and the lake area is based on https://en.wikipedia.org/wiki/Garibaldi_Lake

Approximately 1 trillion litres of water exist in Garibaldi Lake

The Barrier is 1,400 metres tall, so if the 1 trillion litres of water comes crashing down into Squamish.

The lava barrier is an unstable dam for this big lake. The potential energy is 200 times the energy released by the bomb on Hiroshima.

“If the barrier were to explode or fall apart in an earthquake, the wave that would be produced by all that water flowing out of Garibaldi Lake down into Squamish would be 120 metres high,”

-Steve Quane from Quest University

Who did a \$12,000 study in July 2014, to map and assess the danger of Garibaldi Lake.

potential energy is the water behind the Barrier, and kinetic energy (motion) is what happens if the barrier faults, and all the water comes out.

http://www.michigandnr.com/publications/pdfs/IFR/manual/SMII%20Chapter12.pdf

http://www.squamishchief.com/news/garibaldi-lake-a-ticking-time-bomb-1.1753732

Math 10 Honors Numbers Summary

In our first unit of math we learned about prime numbers, and we found prime numbers from 1-200. That’s when we used our divisibility rules. We then reviewed the real number system, which we learned last year. We also reviewed what rational and irrational numbers are, and how to determine which is rational and what is irrational. If a number terminates or repeats, then it is a rational number. Fractions are also rational numbers. There are different sizes of infinity, which was pretty fascinating.  We learned the names of the different parts of a radical are.