Area and Radius of Circles

The video tutorial explains the relationship between a circle's area and its radius, using pi as the constant of variation. It demonstrates how to graph the area against the radius on a Cartesian plane, calculate and plot values, and discusses the proper names of mathematical symbols. The lesson concludes with an analysis of the graph, highlighting the parabolic shape and comparing it to exponential growth.

What is the constant of variation when comparing a circle's area to its radius?

• e

• k

• pi

• r

How does the area of a circle vary with its radius?

• Inversely with the radius

• Directly with the square of the radius

• Directly with the radius

• Inversely with the square of the radius

Which axis is used to represent the radius in the Cartesian plane?

• Vertical axis

• Horizontal axis

• Diagonal axis

• None of the above

What shape does the graph of area against radius form?

• Circle

• Line

• Hyperbola

• Parabola

What is the area of a circle when the radius is zero?

• Zero

• One

• Infinity

• Pi

What is the area of a circle when the radius is one?

• 1

• Pi

• 2Pi

• 4Pi

What is the area of a circle when the radius is two?

• 8Pi

• 4Pi

• 12.57

• 16Pi

What is the name of the symbol commonly referred to as the square root symbol?

• Radical

• Radix

• Radial

• Root

How does exponential growth compare to the growth of a circle's area with radius?

• Exponential growth is faster

• Both grow at the same rate

• Exponential growth is slower

• Circle's area grows faster

What does the term 'area against radius' mean in the context of the graph?

• Area is on both axes

• Neither area nor radius is on the axes

• Radius is on both axes

• Area is one axis and radius is the other