Podcast
Questions and Answers
Imagine rotating a rectangle around one of its sides. Describe the resulting 3D solid and how its dimensions relate to the rectangle's dimensions.
Imagine rotating a rectangle around one of its sides. Describe the resulting 3D solid and how its dimensions relate to the rectangle's dimensions.
The resulting solid is a cylinder. The side of the rectangle used as the axis of rotation becomes the height of the cylinder, and the other side becomes the radius of the cylinder's base.
A sphere is formed by rotating a two-dimensional shape around an axis. What shape is it, and where should the axis be located?
A sphere is formed by rotating a two-dimensional shape around an axis. What shape is it, and where should the axis be located?
A semicircle rotated around its diameter forms a sphere. The axis of rotation is the line containing the diameter.
A cone is formed by rotating a right triangle around one of its legs. If the leg used as the axis of rotation has length 4 and the other leg has length 3, what are the radius and height of the resulting cone?
A cone is formed by rotating a right triangle around one of its legs. If the leg used as the axis of rotation has length 4 and the other leg has length 3, what are the radius and height of the resulting cone?
The cone has a radius of 3 and a height of 4.
A square with side length 6 is inscribed in a circle. What is the area of the shaded region outside the square but inside the circle? (Express your answer in terms of $\pi$).
A square with side length 6 is inscribed in a circle. What is the area of the shaded region outside the square but inside the circle? (Express your answer in terms of $\pi$).
A regular hexagon has a side length of 4. It is made up of 6 equilateral triangles. What is the exact area of this hexagon (leave in simplified radical form)?
A regular hexagon has a side length of 4. It is made up of 6 equilateral triangles. What is the exact area of this hexagon (leave in simplified radical form)?
Flashcards
Solid of Rotation
Solid of Rotation
A 3D shape created by rotating a 2D shape around an axis.
Sphere
Sphere
A round, 3-dimensional object with every point on its surface equidistant from its center.
Cone
Cone
A 3D shape with a circular or oval base tapering to a point.
Cylinder
Cylinder
Signup and view all the flashcards
Octagon
Octagon
Signup and view all the flashcards
Study Notes
- To sketch the solid of rotation, rotate a two-dimensional figure around a horizontal line.
- To create a barrel shape from a 2 dimensional rotation, rotate around a vertical axis.
Matching 2D Figures with Solids of Rotation
- A triangle rotated around an axis forms a cone.
- A rectangle rotated around an axis forms a cylinder.
- A semi-circle rotated around an axis forms a sphere.
Area of a Shaded Region
- The area of the shaded region can be found using given measurements, such as 3.
Area of a Figure with a 70° Angle and Side Lengths of 8 and 10
- The area can be found using the measurements provided.
Regular Octagon
- Stop sign is a regular octagon with sides of 12 inches.
- Area and the perimeter can be determined.
Right Triangle ABC
- Given a right triangle ABC, expressions equal to the length of side BC can be selected from a list of options.
- The triangle includes side lengths: 4.9 and 6.
- Angle B is reported as 55°.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
Explore solids of rotation, matching 2D figures with their 3D counterparts. Practice calculating the area of shaded regions, figures with specific angles, and regular octagons. Work with right triangles to determine side lengths using given angles.
