Geometry: 3d and 2d shapes
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47 Terms
What shape is this?
Cylinder
What shape is this?
Hemisphere
What shape is this?
Pyramid
What shape is this?
cone
What shape is this?
Sphere
What shape is this?
Rectangular prism
What shape is this?
cube
What is a radius?
A radius is a line segment or its length that extends from the center of a circle or sphere to its circumference or surface, and it is always half the length of the diameter.
What is a diameter?
The diameter of a circle is a straight line segment that passes through the circle's center, connecting two points on the circle's opposite edges. It is always twice as much as the radius.
What 3d shape will form after rotating the rectangle continuously around one of its vertical sides (out of the flat plane)
What is its radius and diameter?
A cylinder.
radius = 2
diameter = 4
What 3d shape will form after rotating the triangle continuously around one of its vertical sides (out of the flat plane).
What is its radius and diameter?
A cone.
Radius = 2
Diameter = 4
at 3d shape will form after rotating the circle continuously around one of its vertical sides (out of the flat plane).
What is its radius and diameter?
A sphere.
Radius = 3
diameter = 6
Rotate Triangle ABC continuously around line AC. What shape does it become?
What is its Radius, diameter and height?
A cone.
Height = 4
Radius= 3
diameter = 6
Rotate the rectangle continuously around the vertical line. What shape does it become?
What is its Radius, diameter and height?
It becomes a cylinder.
Height = 4
Radius = 3
Diameter = 6
If a circle is continuously rotated about its diameter, it becomes a…
Sphere
If a half circle is continuously rotated about its diameter, it becomes a…
Sphere
Triangle ABC represents a metal flag on pole AD, as shown in the accompanying diagram. On a windy day the triangle spins around the pole so fast that it looks like a three dimensional shape.
What shape would the spinning flag create?
A cone.
A student has a rectangular postcard that he folds in half lengthwise. Next, he rotates it continuously about the folded edge. Which three-dimensional object is generated by this rotation.
A cylinder
If the rectangle below is continuously rotated about side w, which solid figure is formed?
A cylinder
Which object is formed when the triangle RST is rotated around leg RS ?
A cone
Circle O is centered at the origin. In the diagram, a quater of circle O is graphed.
Which tree-dimensional figure is generated when the quarter circle is continuously rotated about the y-axis?
A hemisphere
If a rectangle is continuously rotated around one of its sides, what is the three-dimensional figure formed?
A cylinder
An equilateral triangle is continuously rotated around one of its altitudes. The three-dimensional object formed is a…
cone
A circle is continuously rotated about its diameter. Which three dimensional object will be formed?
A sphere
As shown in the diagram, right triangle ABC has side lengths of 8 and 15.
If the triangle is continuously rotated about AC, the resulting figure will be…
1). A right cone with a radius of 15 and a height of 8
2) a right cone with a radius of 8 and a height of 15
3) a right cylinder with a radius of 15 and a height of 8
4) a right pyramid with a radius of 8 and a height of 15
1). A right cone with a radius of 15 and a height of 8
Find the volume of RIght triangle ABC if it is rotated continuously about side AC.
Hint: use a formula
600π
When looking for the volume in a 3dd shape what does answering (in terms of pi) mean?
Leaving the answer with the π symbol in it.
What is the cone formula?
V = (1/3)πr2h
What is the sphere formula?
V = 4/3πr3
Square MATH has a side length of 7 inches. What three-dimensional object will be formed by continuously rotating square MATH around side AT, and what is its radius? Find the volume of the shape as well.
Hint: you need a formula
A cylinder with a radius of 7, and its volume is 1077.57
(Note: a square is the same length on all sides)
Which three dimensional figure will result when a rectangle 6 inches long and 5 inches wide is continuously rotated about the longer side?
1) a rectangular prism with a length of 6 inches, width of 6 inches and height of 5 inches.
2) a rectangular prism with a length of 6 inches, width of 5 inches, and height of 5 inches.
3) A cylinder with a radius of 5 inches and a height of 6 inches.
4) a cylinder with a radius of 6 inches and a height of 5 inches.
Then, find the volume of that shape.
3) A cylinder with a radius of 5 inches and a height of 6 inches.
Volume is roughly 471.239
In right triangle CAB, CA = 4 and AB = 6
Determine and state, to the nearest tenth, the volume of the three-dimensional solid formed by rotating CAB continuously around AB.
V = 100.5
What is the cylinder formula?
V = πr2h
What is the cylinder formula?
V = πr2h
What is the cylinder formula?
V = πr2h
What is the cone formula?
V = (1/3)πr2h
What is the cone formula?
V = (1/3)πr2h
What is the sphere formula?
V = (4/3)πr3
What is the sphere formula?
V = (4/3)πr3
46.1 units3
33.5 units3
235.6 units3
564.4 units3
(in terms of PI)
32π
1) long side
2) short side
3) vertical line of symmetry
4) horizontal line of symmetry
3) vertical line of symmetry
335.1
An equilateral triangle is continuously rotated
around one of its altitudes. The three-dimensional
object formed is a…
CONE
Note 
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