Volume of Cubes and Spheres

The video tutorial covers Activity Three from Lesson Seven, focusing on comparing the volumes of a cube and a sphere. It explains how to calculate the volume of a cube using the edge length and the volume of a sphere using a graph. The tutorial presents three problems: comparing volumes when the edge length and radius are equal, finding the sphere's radius when volumes are equal, and comparing volume functions with specific inputs. The video emphasizes understanding the relationship between the volumes of cubes and spheres.

How do you calculate the volume of a cube if the edge length is given?

• Multiply the edge length by 4

• Square the edge length

• Multiply the edge length by 2

• Cube the edge length

What is the volume of a cube with an edge length of 3 units?

• 18 cubic units

• 27 cubic units

• 36 cubic units

• 9 cubic units

How is the volume of a sphere determined using a graph?

• By measuring the diameter

• By reading the radius and using a formula

• By reading the radius, then reading up and over to the y-axis

• By calculating the circumference

When the edge length of a cube is 3 units, how does its volume compare to a sphere with a radius of 3 units?

• The sphere's volume is greater

• The cube's volume is greater

• Both have the same volume

• The cube's volume is twice the sphere's volume

If a cube and a sphere have the same volume, and the cube's edge is 5 units, what is the approximate radius of the sphere?

• 3.1 units

• 5.0 units

• 2.5 units

• 4.5 units

What is the volume of a cube with an edge length of 5 units?

• 100 cubic units

• 125 cubic units

• 150 cubic units

• 175 cubic units

What is the output when the input is the radius of a sphere in a volume function?

• The volume

• The circumference

• The diameter

• The surface area

For a sphere with a radius of 2 units, what is the approximate volume?

• 48 cubic units

• 35 cubic units

• 24 cubic units

• 16 cubic units

When the radius of a sphere and the edge of a cube are both 2 units, how do their volumes compare?

• The sphere's volume is twice the cube's volume

• Both have the same volume

• The cube's volume is slightly more than four times the sphere's volume

• The sphere's volume is slightly more than four times the cube's volume

What will be discussed in lesson 20?

• The volume of spheres

• The area of triangles

• The surface area of cubes

• The circumference of circles