My Studies Diary


Volume of Objects

Volume = area of base x height

Area of Base = length x width

To work out the volume of a cone, vs a cylinder, we work out the volume of the cylinder and then divide by 3. The volume of a cone is a third of a cylinder.

Volume of cylinder = π * r ^2 * h
Volume of sphere = ⁴⁄₃πr³
 the volume of a cone is pi times the radius squared times the height divided by 3


Angles & Triangles

supplementary angle – either of two angles whose sum is 180°.

When two lines are crossed by another line (called the Transversal), the angles in matching corners are called Corresponding Angles.

complementary angles – either of two angles whose sum is 90°.
Vertical Angles are the angles opposite each other when two lines cross. “Vertical” in this case means they share the same Vertex (corner point), not the usual meaning of up-down.

All squares have four right angles and four sides that are equal in length.

Equilateral definition, having all the sides equal: an equilateral triangle.

For a triangle to be equilateral, it must also have equal angles. Every triangle’s three angles sum to 180. 180 divided by 3 is 60. 60 is less than 90. Angles are either right, which is to say 90 exactly, or obtuse, which is to say greater than 90 and less than 180, or acute, which is to say less than 90. An acute triangle is one in which all three angles are acute. Equilateral triangles are all acute.

isosceles triangle is a triangle that has two sides of equal length. an equilateral triangle is a triangle in which all three sides are equal. A scalene triangle is a triangle that has three unequal sides.

An acute triangle (or acute-angled triangle) is atriangle with three acute angles (less than 90°). An obtuse triangle is a triangle in which one of the angles is an obtuse angle.

Circle Pi Area Circumference & More

The circumference is the outside perimeter of a circle. It’s the distance around a circle. A radius can be a line from any point on the circumference to the center of the circle. If you put two radii together, edge to edge, going through the center of a circle, you would get a diameter.

We have a formula that relates these two parts of a circle. This formula is called the circumference formula, and it is C = pi*d where C stands for the circumference and d stands for the diameter. And pi is pi or 3.14.

Formula for Area of circle. The formula to find a circle’s area (radius)2 usually expressed as π ⋅ r 2 where r is the radius of a circle. The area of a circle is all the space inside a circle’s circumference.

Circumference: C=π⋅d or C=2π⋅r

Area: A=πr2
The volume of a rectangular prism can be found by multiplying the area of a base by the corresponding height.
Volume = area of base x heigh


While  so does  How do we know which form to use? When writing normalized scientific notation, the coefficient must be greater than 1 and less than 10.

Take 835,000

Move the decimal point to the first digit, so 8.35000 and then count how many places after the decimal point. There are 5 places after the decimal point so this number is 10^5.

So we get 8.35 x 10^5.

This is cold scientific notation and it is a method of representing very large or very small numbers.

Also written using E