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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
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Octagon
Octagon
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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°.
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