[size=200][size=85][size=100][left]A cube is a three-dimensional shape that has six square faces. All edges of a cube have the same length, and all angles are right angles.[br]Examples of cube-shaped objects include dice, Rubik’s cubes, and ice cubes.[br]Elements of a Cube[br]A cube has several important parts:[br]Faces:[br]A cube has 6 square faces.[br]Edges:[br]A cube has 12 edges with equal lengths.[br]Vertices:[br]A cube has 8 vertices or corner points.[br]Face Diagonals:[br]A cube has 12 face diagonals.[br]Space Diagonals:[br]A cube has 4 space diagonals.[br]Diagonal Planes:[br]A cube has 6 diagonal planes.[br]A cube net is a two-dimensional pattern that can be folded to form a cube. There are many different cube net patterns, but not all arrangements of squares can form a cube.[br]The surface area of a cube is the total area of all six square faces.[/left]Formula:[br]Surface Area = [math]6s^2[/math][/size][/size][/size][br]Formula:[br]Volume = [math]s^3[/math][br][br]Diagonals of a Cube:[br][br]Face Diagonal[br]A face diagonal is a line connecting two opposite corners on the same face of the cube.[br]Formula:[br]Face Diagonal = [math]s\times\sqrt{2}[/math][br]Space Diagonal[br]A space diagonal is a line connecting two opposite vertices through the inside of the cube.[br]Formula:[br]Space Diagonal = [math]s\times\sqrt{3}[/math]

[math][/math]A cuboid is a three-dimensional shape that has three pairs of rectangular faces. The opposite faces have the same size and shape.[br][br]Examples of cuboid-shaped objects include boxes, bricks, cupboards, and aquariums.[br][br]Elements of a Cuboid[br]Faces[br]A cuboid has 6 rectangular faces.[br]Edges[br]A cuboid has 12 edges.[br]Vertices[br]A cuboid has 8 vertices.[br]Face Diagonals[br]A cuboid has 12 face diagonals.[br]Space Diagonals[br]A cuboid has 4 space diagonals.[br]Diagonal Planes[br]A cuboid has 6 diagonal planes.[br][br]A cuboid net is a two-dimensional pattern that can be folded into a cuboid. The net consists of rectangles arranged in certain forms.[br][br]The surface area of a cuboid is the total area of all its faces.[br]Formula:[math]\text{SA=2(pl+pt+lt)}[/math][br]Where:[br]SA = surface area[br]p = length[br]l = width[br]t = heigh[br]l = width[br]t = height[br][br]The volume of a cuboid is the amount of space inside the cuboid.[br]Formula:[math]\text{V=p×l×t}[/math][br]Where:[br]V = volume[br]p = length[br]l = width[br]t = height[br][br]Diagonals of a Cuboid[br]Face Diagonal[br]A face diagonal is a line connecting two opposite vertices on the same face.[br]Formulas: [math]d=\sqrt{p^2+t^2}[/math] and [math]d=\sqrt{p^2+t^2}[/math] and [math]d=\sqrt{l^2+t^2}[/math][br]Space Diagonal[br]A space diagonal is a line connecting two opposite vertices through the inside of the cuboid.[br]Formula: [math]d=\sqrt{p^2+t^2+l^2}[/math]

Definition of a Cylinder[br]A cylinder is a three-dimensional shape that has two parallel circular bases connected by a curved surface.[br]Examples of cylinder-shaped objects include cans, pipes, drums, and water bottles.[br]Elements of a Cylinder[br]Bases[br]A cylinder has 2 circular bases, one at the top and one at the bottom.[br]Curved Surface[br]A cylinder has 1 curved surface connecting the two bases.[br]Radius[br]The radius is the distance from the center of the circle to its edge.[br]Diameter[br]The diameter is twice the radius.[br]Formula:[br][math]d=2r[/math][br]Height[br]The height is the distance between the two circular bases.[br]Net of a Cylinder[br]A cylinder net consists of:[br]two circles[br]one rectangle representing the curved surface[br]Students should understand how the net forms a cylinder when folded.[br]Surface Area of a Cylinder[br][br]The surface area of a cylinder is the total area of all its surfaces.[br]Formula:[br][math]\text{SA=2πr(r+t)}[/math][br]Where:[br]SA = surface area[br]r = radius[br]t = height[br][math]\pi=3,14[/math] or [math]\frac{22}{7}[/math][br]Students should practice:[br]calculating surface area[br]finding radius or height[br]solving word problems[br]Volume of a Cylinder[br][br]The volume of a cylinder is the amount of space inside the cylinder.[br]Formula:[br][math]\text{V=πr[br]2[br]t}[/math][br]Where:[br]V = volume[br]r = radius[br]t = height[br]Students should practice:[br]calculating volume[br]finding dimensions from volume[br]solving real-life problems[br]Circumference of the Base Circle[br]The circumference of the circular base can be calculated using:[br][math]\text{[br]K=2πr}[/math][br]or[br][math]\text{K=πd}[/math][br]Where:[br]K = circumference[br]r = radius[br]d = diameter

Elements of a Cone[br]Base[br]A cone has 1 circular base.[br]Vertex[br]A cone has 1 vertex or apex at the top.[br]Radius[br]The radius is the distance from the center of the base to the edge of the circle.[br]Diameter[br]The diameter is twice the radius.[br]Formula:[br][math]\text{d=2r}[/math][br]Height[br]The height is the perpendicular distance from the vertex to the center of the base.[br]Slant Height[br]The slant height is the distance from the vertex to the edge of the circular base.[br]Formula:[br][math]\text{s=\sqrt{r2+t2}}[/math][br]Where:[br]s = slant height[br]r = radius[br]t = height[br]Net of a Cone[br]A cone net consists of:[br]one circle as the base[br]one sector of a circle as the curved surface[br]Students should understand how these parts form a cone when folded.[br]Surface Area of a Cone[br]The surface area of a cone is the total area of the base and the curved surface.[br]Formula:[br][math]\text{SA=πr(r+s)}[/math][br]Where:[br]SA = surface area[br]r = radius[br]s = slant height[br]Students should practice:[br]calculating surface area[br]finding slant height[br]solving word problems[br]Volume of a Cone[br]The volume of a cone is the amount of space inside the cone.[br]Formula:[br][math]\text{V=\frac{1}{3}​πr2t}[/math][br]Where:[br]V = volume[br]r = radius[br]t = height[br]Students should practice:[br]calculating volume[br]finding dimensions from volume[br]solving real-life application problems[br]Circumference of the Base Circle[br]The circumference of the base circle can be calculated using:[br][math]\text{K=2πr}[/math][br]or[br][math]\text{K=πd}[/math][br]Where:[br]K = circumference[br]r = radius[br]d = diameter