Volume of Cubes and Spheres

The video tutorial covers activity three from lesson seven, focusing on comparing volumes of cubes and spheres. It explains how to calculate the volume of a cube using its edge length and how to use graphs to find the volume of a sphere based on its radius. The tutorial presents three problems: comparing volumes of a cube and a sphere with the same dimensions, determining the radius of a sphere with the same volume as a cube, and comparing volume functions with specific inputs. The video emphasizes understanding the relationship between the dimensions and volumes of these shapes.

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

• Double the edge length

• Cube the edge length

• Square the edge length

• Multiply the edge length by 4

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

• 9 cubic units

• 81 cubic units

• 3 cubic units

• 27 cubic units

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

• By measuring the diameter

• By calculating the circumference

• By reading the radius and using a formula

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

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?

• 2.5 units

• 4 units

• 3.1 units

• 5 units

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

• 100 cubic units

• 125 cubic units

• 25 cubic units

• 150 cubic units

When the input is 2 units, what is the volume of the sphere?

• 8 cubic units

• 16 cubic units

• 27 cubic units

• 35 cubic units

What is the volume of a cube with an edge length of 2 units?

• 8 cubic units

• 16 cubic units

• 2 cubic units

• 4 cubic units

What is the independent variable when comparing the volumes of a cube and a sphere?

• The diameter

• The surface area

• The radius or edge length

• The volume

What is the relationship between the volume of a sphere and a cube when their dimensions are equal?

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

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

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

• The sphere's volume is equal to the cube's volume

What will be discussed in lesson 20?

• The area of triangles

• The circumference of circles

• The volume of spheres

• The surface area of cubes