Exploring Volumes of 3D Shapes

What is volume?

• The surface area of an object

• The amount of space inside a solid

• The length of an object

• The weight of an object

What units are used to measure volume?

• Cubic units

• Linear units

• Square units

• Kilograms

How do you calculate the volume of a cylinder?

• Pi times radius squared times height

• Radius times height

• Base area times height

• Length times width times height

What principle allows us to calculate the volume of slanted objects?

• Pythagorean theorem

• Euler's formula

• Cavalieri's principle

• Archimedes' principle

What does Cavalieri's principle state about volumes?

• Equal volumes have equal heights

• Volumes can be added together

• Solids with equal cross-sections have equal volumes

• Volume is independent of width

What is the volume formula for a cone?

• Base area times height

• Base area times height divided by 3

• Pi times radius squared times height

• 1/3 times pi times radius squared times height

What is the relationship between the volume of a cone and a cylinder with the same base and height?

• The volume of the cone is one-third of the cylinder

• The volume of the cylinder is twice the cone

• The volume of the cone is three times the cylinder

• The volume of the cylinder is the same as the cone

What is the surface area formula of a sphere?

• Pi r squared

• 4 pi r cubed

• 2 pi r squared

• 4 pi r squared

How is the volume of a sphere calculated?

• 4/3 pi r cubed

• 4 pi r squared

• Pi r squared times height

• 2/3 pi r cubed

How can you find the radius of a sphere if you know its volume?

• Cube root of (3 volume / 4 pi)

• Cube root of (volume / pi)

• Square root of (volume / pi)

• Volume divided by pi