Geometry: Surface Areas and Volumes

Study Notes

Surface Area of a Cube: 6a^2, where a is the side length
Surface Area of a Cuboid: 2(lb + bh + lh), where l, b, and h are the length, breadth, and height respectively
Surface Area of a Sphere: 4πr^2, where r is the radius
Volume of a Cube: a^3, where a is the side length
Volume of a Cuboid: lbh, where l, b, and h are the length, breadth, and height respectively
Volume of a Sphere: (4/3)πr^3, where r is the radius
Volume of a Cylinder: πr^2h, where r is the radius and h is the height
Volume of a Cone: (1/3)πr^2h, where r is the radius and h is the height

Circumference of a Circle: 2πr, where r is the radius
Area of a Circle: πr^2, where r is the radius
Sector of a Circle: A sector is a region bounded by an arc and two radii
Segment of a Circle: A segment is a region bounded by an arc and a chord
Circle Theorems:
- The angle at the center of a circle is twice the angle at the circumference
- The angle in a semicircle is a right angle
- Angles in the same segment are equal
- The angle of a cyclic quadrilateral is supplementary to the angle at the center of the circle

Quadratic Equation: A polynomial equation of degree two, in the form ax^2 + bx + c = 0
Roots of a Quadratic Equation: The values of x that satisfy the equation
Factorization Method: Factorizing the quadratic equation into the product of two binomials
Quadratic Formula: x = (-b ± √(b^2 - 4ac)) / 2a
Graph of a Quadratic Equation: A parabola that opens upwards or downwards

Trigonometric Ratios:
- sine (sin): opposite side / hypotenuse
- cosine (cos): adjacent side / hypotenuse
- tangent (tan): opposite side / adjacent side
Trigonometric Identities:
- sin^2A + cos^2A = 1
- tanA = sinA / cosA
Trigonometric Values:
- sin(30°) = 1/2
- sin(45°) = 1/√2
- sin(60°) = √3/2
Graphs of Trigonometric Functions:
- sine wave: periodic and oscillatory
- cosine wave: periodic and oscillatory
- tangent wave: periodic and oscillatory

Cube: Surface area = 6a^2, volume = a^3, where a is the side length
Cuboid: Surface area = 2(lb + bh + lh), volume = lbh, where l, b, and h are the length, breadth, and height respectively
Sphere: Surface area = 4πr^2, volume = (4/3)πr^3, where r is the radius
Cylinder: Volume = πr^2h, where r is the radius and h is the height
Cone: Volume = (1/3)πr^2h, where r is the radius and h is the height

Circumference: 2πr, where r is the radius
Area: πr^2, where r is the radius
Sector: Region bounded by an arc and two radii
Segment: Region bounded by an arc and a chord
Circle Theorems:
- Angle at the center of a circle is twice the angle at the circumference
- Angle in a semicircle is a right angle
- Angles in the same segment are equal
- Angle of a cyclic quadrilateral is supplementary to the angle at the center of the circle

Definition: Polynomial equation of degree two, in the form ax^2 + bx + c = 0
Roots: Values of x that satisfy the equation
Factorization Method: Factorizing the quadratic equation into the product of two binomials
Quadratic Formula: x = (-b ± √(b^2 - 4ac)) / 2a
Graph: Parabola that opens upwards or downwards

Trigonometric Ratios:
- sine (sin) = opposite side / hypotenuse
- cosine (cos) = adjacent side / hypotenuse
- tangent (tan) = opposite side / adjacent side
Trigonometric Identities:
- sin^2A + cos^2A = 1
- tanA = sinA / cosA
Trigonometric Values:
- sin(30°) = 1/2
- sin(45°) = 1/√2
- sin(60°) = √3/2
Graphs of Trigonometric Functions:
- sine wave: periodic and oscillatory
- cosine wave: periodic and oscillatory
- tangent wave: periodic and oscillatory