9.5- use Nets and cross-sections to analyze three-dimensional figures
Sphere Volume
4/3πr³
Net of a Cone
A cone has one circular base. The net of a cone is a full circle for the base, and the a part of another circle for the wall of the cone.
orthographic Projection
A method of representing three-dimensional objects on a plane having only length and breadth. Also referred to as Right Angle Projection. https://images.app.goo.gl/AQFSwuiRd1aTpuCQ6
Transformation Congruence
A moved figure that retains the same size, shape, angles, and side lengths of the original image.
cube
A prism with six square faces
triangular pyramid
A tetrahedron with a three-dimensional figure that is a polyhedron that has four triangular faces
cone
A three dimensional shape with a circular base and a vertex opposite the base
geometric solid
A three-dimensional geometric figure, such as a prism, pyramid, cylinder, cone ,or sphere.
Trimetric Projection
An axonometric projection of a three-dimensional object inclined to the picture plane in such a way that all three principal axes are foreshortened at a different rate.
right circular cylinder
An object with a circular base, and a curving side that is perpendicular with the base. v=πr²h
right circular cone
Any cone with circular right section. Whose axis is perpendicular to its base, v=⅓πr²h
diametric projection
Dimetric projection has equal foreshortening along two axis directions. The object is not tipped an equal amount to all of the principle planes of projection...x, y axis 135°
Cuboid
Having the shape of a cube.
net of a sphere
Nets of a sphere cannot be made because it does not have any flat surfaces.
#67 - A net is composed of squares and equilateral triangles. What is the volume of a shape that is generated by folding the net?
The bases of the triangular prism are equilateral triangles of side length one and height √(1²-(½)²= √3 / 4 by application of pythagorean theorem. the area of each triangle is ½ ×Base×height = ½×1×√3/4= 2√3/4; the volume of a prism is found by the area of its base× its height, or √3/4×1= √3/4 cubic units. Competency 9.5- Use nets and cross-sections to analyze 3 dimensional figures.
surface area
The measurement of the outer surface of an object.
Net of a Triangular Pyramid
The net of a triangular pyramid consists of four triangles. The base of the pyramid is a triangle, and the lateral faces are also triangles. The net of a rectangular pyramid consists of one rectangle and four triangles.
Isometric Projection
Three dimensional drawing made up of equal angles of 120 degrees, most common 3-D drawing used in industry.
rectangular solid
V=lwh
cube
V=s³
rectangular prism
a cuboid is a convex polyhedron bounded by 6 quadrilateral faces
quadrilateral
a four-sided polygon
Net of a Prism
a pattern that is seen when the surface of the prism is opened, flattened, and laid out such that all the faces are seen clearly. It is two-dimensional. This net can be folded up to make a triangular prism.
a plane at an angle relative to the base it intersects the base
a plane at an angle relative to the base it intersects the base of a rectangular pyramid will make a cross-section that has four sides. The cross section will have one pair of parallel sides (the side along the base of the pyramid and the opposite side a long one triangular face) and one pair of sides that are not parallel along two opposite triangular faces. So, the cross section is a trapezoid.
pentagonal prism
a prism with a pentagon as its base with 5 triangular faces that meet at a point (the vertex).
regular square pyramid
a pyramid w/ a square base, v=⅓s²h
square pyramid
a pyramid with a square base....has 5 faces
rectangular pyramid
a solid figure with a rectangle for its base a polyhedron formed by connecting a polygonal base and a point called the Apex.
Net of a Cylinder
is formed of two circles, with one attached to each end of a rectangle.
if asphalt pavement cost $0.90 per square foot find the cost to pay there at circular Road where a=60 and b=50 of the triangle.
larger circle-πr²= π50²=2500π Inner circle- πr²= π60²=3600π 11310-7854=3456 3456×.90= $3110.40
which of the following shapes could not be a cross section of the prism?
octagon. an octagon cannot be a cross section of the rectangular prism, because a rectangular prism has only six faces and an octagon has eight sides.
pentagonal pyramid
pyramid with a Pentagonal (five sided) base that meet at a point, star net...
hexagonal pyramid
solid shape whose base is a hexagon and 6 triangular(isosceles) faces that meet at a point.
earth science - crystals are solids in which the atoms are arranged in rectangular geometrical patterns. Sketch a cross section from a horizontal slice of each Crystal. Then describe the rotational symmetry about the vertical axis.
tetragonal. A cross-section from a horizontal slice will look just like the top view of the figure, which appears to be a square. Like all squares, a 90° rotation will produce an image identical to the preimage. The crystal appears the same for every 90 degree rotation about the axis.
Eduardo has a piece of wood in the shape of a square pyramid. The sides of the base are 6 in Long. Eduardo cuts the pyramid with a single straight cut parallel to the base. Which of the following statements about the cross-section must be true.
the cross section is a square with an area less than 36in². any Square formed by the cross section of this pyramid, that isn't the base, will have a smaller area than the base since the lateral faces of the pyramid slope in until they meet at the vertex.
cross section
the intersection of a three-dimensional figure and a plane surface or shape that is or would be exposed by making a straight cut through something
a square pyramid with a height of 24 cm and a base length of 24 cm intersected by a plane perpendicular to the base of the pyramid and through the vertex. Determine the shape of the cross section?
the shape of the cross-section with a plane intersecting a pyramid perpendicular to the base and through the vertex will make a triangle with a slant height as two sides and the other side is part of the base.