Spheres
Prisms & Cylinders
Pyramids & Cones
3D Figures & Cross Sections
Just the Facts
100
The volume of a sphere is ___ of the product of pi and the cube of the radius of the sphere.
4/3
100
How does Cavalieri's Principle apply to prisms and cylinders?
The cross sections are the same size and shape as its base.
100
According to Cavalieri's Principle, what has to be the same in Pyramids and Cones for the volumes to be equal?
The height and area of every cross section.
100
How does one calculate the number of faces, edges, and vertices in a 3-dimensional figure?
Euler's formula:
F+V=E+2
100
Why is it not possible to rotate a 2-dimensional figure to form a cube?
Any rotation will form a rounded edge.
200
A great circle divides a sphere into two _____.
Hemispheres
200
V=(pir^2)*h
Volume of a cylinder
200
What does the equation represent?
V=1/3Bh
A Cone
200
If the solid is intersected with a plane parallel to the base, what shape would the cross section create?
A Pentagon
200
Rotating a polygon about an axis forms a ___________.
3-dimensional Figure
300
Alex got a new basketball. His new basketball is 10 inches in diameter. What is the volume of the basketball? (Round to 2 decimal places)
523.60 in3
300
This is the formula for a triangular prism.
V=(1/2bh)*h
300
This is the equation of a triangular pyramid.
V=1/3(bh-:2)H
300
If rotated about the hypotenuse, what shape would a right isosceles triangle form?
A Double Cone
300
This formula states that the sum of the faces and vertices of a polyhedron is 2 more than the number of its edges.
F+V=E+2
Euler's Formula
400
Tanner wanted a bowl of cereal. The bowl he chose has a radius of 7 cm. How much cereal could the bowl hold? (Round to 2 decimal places)
718.38 cm3
400
A stack of frisbees is 10 inches tall and 8 inches wide. What is the volume of the cylinder created by the frisbees? (Round to 2 decimal places)
502.65 in3
400
Tommy wanting an ice cream cone. The ice cream parlor has two size cones. The large cone is $5.50 and the small cone is $3.25. Which ice cream cone is the best deal? (Round to 2 decimal places--we are dealing with money!)
small
large 
Small: V= 128.28 cm3
Price/Volume = 0.03/cm3
Large: V = 314.16 cm3
Prcie/Volume = 0.02/cm3
400
A polygon has 10 faces and 20 edges. How many vertices does it have?
10 + V = 20 + 2
V = 20 + 2 - 10
V = 12
400
__________ describes the relationship between the volume of a sphere and the volumes of a cylinder and cone.
Cavalieri's Principle
500
Mr. Graves ordered an ice cream cone. What is the total volume of the ice cream and cone? (Round to 2 decimal places)
169.65 cm3
500
My dog, Diesel, dug a triangular prism shaped hole with both heights equaling 6m with a base of 2m. How much dirt will I need to fill the hole? (Round to 2 decimal places)
36 cubic meters of dirt
500
The Great Pyramid of Giza (a rectangular pyramid) was originally 147 meters tall, and each side was 230 meters. What was the original volume of the Great Pyramid of Giza?
2,592,100 m3
500
A gem cutter cuts polyhedral crystal from garnet gemstones. The crystal has 8 fewer edges as faces and twice as many edges as faces. How many faces, vertices, and edges does the crystal have?
V = E - 8
E = 2F ---> F = E/2
E/2 + E - 8 = E + 2
E/2 = 10
E = 20
V = 20 - 8
V = 12
F + 12 = 20 - 8
F = 10
500
A _______ is the intersection of a convex polyhedron and a plane; a polygon.
Cross-Section