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December 1st 2021
Cone and cylinder volumes
Cone and cylinder volumes
Today we were learning how to find the volume of a cylinder and a cone, and look for the relationship between the two.
The variables are -
V = Volume
r = Radius
H = Height
Graph 1 - Fixed radius of 7, changing height
The formula to find the volume of a cylinder is V = πr2 h
The formula to find the volume of a cone is V = (πr2 h) / 3
Our radius stayed at 7, and the height was between 1 and 10. Our formula looked like this once we plugged in the numbers for the cylinder - V = π72 2
We ended up noticing that the volume increased by 51.31 each time the height increased.
Graph 2 - Fixed height of 7, changing radius
The formulas are the same, but now the height is fixed at 7 and the radius can be plugged in.
Cylinder is V = πr2h
Cone is V = (πr2h)/3
Our formula looked like this once we plugged in the numbers for the cylinder - V = π32 7
The difference between the volumes varied and became larger each time, unlike when the radius was the fixed number. Then we decided to find the difference of the difference and it was 14.66 each.
November 23rd 2021
The Pythagorean Theorem was named after a Greek philosopher named Pythagorus, It was believed that he was the first to discover this formula for triangles, but that is not ture. Many civilizations before his time had used this method to build pyramids and temples, and because pythagoras was technically not the creator, the other name for it is The Side Relationship For Right Triangles.
The way to solve for side C in a right angle triangle is to use the equation
a2 + b2 = c2. You can also use this formula to see if a triangle has a right angle.
November 23rd 2021
Circle and Triangle Angle Relationships
Circle and Triangle Angle Relationships
Central angle - Angle that stays in the center of circle that the shape is in
Inscribed angle - Angle that has a 0.5 difference relationship with the central angle. Always half of the central angle unless it is on the arc, then it becomes a larger obtuse angle
Subtended angle - Angle is congruent and branches off of the central angle to create an arc
The inscribed angle is A (136)and the central angle is O (68). The subtended angle is angle B,O,C, and branches off of the central angle to create an arc.
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