List of all equations
Area of a trapezoid: A = ½ (b1 + b2) h
Area of a circle: A = πr²
Surface area of a prism: SA = 2B + Ph (B is the area of the base. P is the perimeter of the base).
Surface area of a cylinder: SA = 2B + Ch (B is the area of the base, πr². C is the circumference of the base, which would equal 2πr. So it would be SA = 2πr² + 2πrh ).
Surface area of a pyramid: SA = B + ½Pl (B is the area of the base. P is the perimeter of the base).
Surface area of a cone: SA = πr² + πrl
Surface area of a sphere: SA=4πr²
Volume of a prism: V = Bh (B is the area of the base).
Volume of a cylinder: V = Bh (B is the area of the base, which is πr². So it's V = πr²h).
Volume of a pyramid: V = ⅓Bh (B is the area of the base).
Volume of a cone: V = ⅓Bh (B is the area of the base, which would be πr². So, it's
V = ⅓πr²h
Volume of a sphere: V = 4/3πr³
Slant height: a² + b² = c²
Area: The number of square units covered by a figure.
Base: The surface a solid object stands on, or the bottom line of a shape such as a triangle or rectangle.
Height: Height is a measure of a polygon or solid figure, taken as a perpendicular from the base of the figure.
Circle: A 2-dimensional shape made by drawing a curve that is always the same distance from a center.
Radius: The distance from the center to the edge of a circle. It is half of the circle's diameter.
Pi: The ratio of a circle's circumference to its diameter. Equal to 3.14159265358979323846... (the digits go on forever without repeating)
Trapezoid: A 4-sided flat shape with straight sides that has a pair of opposite sides parallel.
Parallelogram: A 4-sided flat shape with straight sides where opposite sides are parallel.
Rhombus: A 4-sided flat shape with straight sides where all sides have equal length. Also opposite sides are parallel and opposite angles are equal.
Diameter: A straight line going through the center of a circle connecting two points on the circumference.
Circumference: The circle that passes through all vertices (corner points) of a regular polygon. Its radius is also the radius of the regular polygon.
Solid: A three dimensional (3D) object. The 3 dimensions are called width, depth and height. Examples include, spheres, cubes, pyramids and cylinders.
Prism: A solid object with two identical ends and flat sides. The sides are parallelograms (4-sided shape with opposites sides parallel). The cross section is the same all along its length. The shape of the ends give the prism a name, such as "triangular prism" It is also a polyhedron.
Cylinder: A solid object with two identical flat ends that are circular or elliptical and one curved side. It has the same cross-section from one end to the other.
Cone: A solid (3-dimensional) object with a circular base and one vertex.
Sphere: A 3-dimensional object shaped like a ball. Every point on the surface is the same distance from the center.
Net: A pattern that you can cut and fold to make a model of a solid shape.
Surface Area: The total area of the surface of a three-dimensional object. Example: the surface area of a cube is the area of all 6 faces added together.
Slant Height: The diagonal distance from the apex of a right circular cone or a right regular pyramid to the base.
Volume: The amount of 3-dimensional space an object occupies. Capacity.
Pyramid: A solid object where the base is a polygon (a straight-sided flat shape) and the sides are triangles which meet at the top (the apex).
Polyhedron: A solid that is enclosed with polygons.
Edges of a polyhedron: A line segment where two faces of a polyhedron meet.
Vertices of a polyhedron: Where the corners of two or more faces meet. (A corner).
Finding Slant Height
Areas of parallelograms and trapezoids
The area of a parallelogram is found when you multiply the base and the height.
The area of a trapezoid is one half the product of the sum of the bases and the height.
Equation: A = 1/2( b1 + b2 )h
Areas of Circles
The area of a circle is the product of π and the square of the radius.
Formula: A = πr²
Surface Areas of Prisms and Cylinders
The surface area of a prism is the the sum of the twice the area of the base, B, and the product of the base's perimeter P and the height h.
Formula: S = 2B + Ph
----------The B changes depending on the base.
To the right: The Perimeter is the BASE'S perimeter
The surface area of a cylinder is the sum of twice the area of A base, B, and the product of the base's circumference, C, and the height, H.
Equation: SA = 2B + Ch. B is the area of the base, πr². C is the circumference of the base, which would equal 2πr. So it would be SA = 2πr² + 2πrh
Surface Areas of Pyramids and Cones
Surface Area of a PyramidThe surface area of a rectangular pyramid is the sum of the area of the base, B, and one half the product of the base perimeter, P, and the slant height, l.
Equation: SA = B + 1/2Pl
B stands for the area of the base, and P stands for the perimeter of the base.
The surface area of a cone is the sum of the area of the circular base with radius, r, and the product of pi, the radius r of the base, and the slant height l.
Equation: SA = πr² + πrl
In the video, s is the same as l in the equation above.
Volumes of Prisms and Cylinders
The volume of a prism is the product of the area of the base, B, and the height, h.
Equation: V = Bh
B varies based on the shape of the base.
The volume of a cylinder is the product of the area of the base, B, and the height, H.
Equation: V = Bh
(B is really); πr²
Full equation: V = (πr²)h
Volumes of Pyramids and Cones
The volume, V, of a pyramid is one third the product of the area of the base, B, and the height, h.
Equation: V = 1/3Bh
The volume of a cone, V, is one third the product of the area of the base, B, and the height, h.
Equation: V = 1/3Bh
*simplified: V = 1/3(πr²)h
Volume of a Sphere
The volume, V, of a sphere is four thirds the product of π and the cube of the radius, r.
Equation: V = 4/3πr³