Modeling 3D Objects
Cross Sections of 3D Objects
Rotations of 2D Objects
Informal Volume Arguments
Word Problems
100
These two objects can be modeled with a cylinder.
What is a can of soda, roll of quarters, paper towel roll, etc.
100
This cross sectional shape is not possible when a cone is cut by a plane: circle, ellipse, trapezoid, triangle.
What is a trapezoid.
100
This three-dimensional figure is created when you rotate a triangle on any axis.
What is a cone.
100
This is the height of a rectangular pyramid with length and width of 9mm and volume of 324 mm^3.
What is 12 mm.
100
Find the volume of a cone with a base circumference of 81 m and a height of 88 m. (Use 3.14 and round to the nearest tenth at every step).
What is 15,327.5 m^3.
200
The Louvre in France represents this geometric figure.
What is a square pyramid.
200
We can cut a rectangular pyramid in what relation to the base to get a cross section shaped like a trapezoid (Name the cut and the location).
What is perpendicular to the base not through the central point.
200
This is the radius of the shape that is created when an equilateral triangle with bottom edge of 4 cm is rotated about the y-axis through the central point.
What is 2 cm.
200
This is the volume of a cone with a radius of 7cm and height of 30cm (Use 3.14)
What is 1538.6 cm^3.
200
David is sitting at a desk with dimensions 25 x 17 x 5 inches. He was wondering how many notebooks could fit inside. Each notebook is 9 x 10 x 1 inches. How many whole notebooks can fit in the desk?
What is 23 notebooks.
300
This is the top view of a triangular prism that is laying on its long side.
What is a rectangle.
300
A square prism laying on its longer side has a vertical cross section of this shape.
What is a square.
300
This is the base area of the shape that is created when a square with side length 3cm is rotated around the x-axis on edge (Use 3.14 and round to the nearest tenth).
What is 28.3 cm^2.
300
A pyramid has a volume of 16 m^3. What is the volume of a rectangular prism with the same length, width, and height?
What is 48 m^3.
300
At SkyZone, there are 4,000 sponge cubes in the foam pit. if each cube has an edge of 5 inches, what is the total volume of all of the sponge cubes?
What is 500,000 in^3
400
This geometric figure has a triangle for a top, side, and front view.
What is a triangular pyramid.
400
This is the area of the parallel cross section of a cube with a volume of 27,000 cm^3.
What is 900 cm^2.
400
This is the volume of the figure that is created when a circle with a radius of 15 cm is rotated (Name the figure and the volume, use 3.14).
What is a circle with a volume of 14130 cm^3.
400
A square pyramid has a height of 12 in and base area of 4 in^2. A rectangular prism has the same height and base area. Do they have equal volumes according to Cavalieri's Principle? Why or why not?
What is No, the parallel cross sections of the square pyramid do not equal the parallel cross sections at the same height of the prism (other than the base).
400
Cone A has a slant height of 6 mm and a diameter of 3 mm. Cone B has a height of 5 mm and a diameter of 4 mm. Which cone holds the least amount? (Use 3.14 and round to the tenth at every step).
What is Cone A
500
This geometric figure has rectangular front and side views and a triangular top view.
What is a triangular prism.
500
This is the shape of the cross section derived from cutting a plane diagonal to and through the base on a cone.
What is a semicircle.
500
This is the volume of the figure that is created when a rectangle with a length of 3m and height of 5m is rotated (Name the figure and the volume, use 3.14 and round to the nearest tenth).
What is cylinder with a volume of 35.3 m^3.
500
A cylinder and an oblique rectangular prism have base areas of 12 m^2. According to Cavalieri's Principle, what else do they need to have equal volumes?
What is same height.
500
Find the circumference of a sphere with a volume of 33.5 in^3 (Use 3.14 and round the radius to the nearest whole number).
What is 12.56 in.
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