Quiz – Why the Area of a Circle is \(\pi r^2\) (Visual Explanation)

Test your understanding of why the area of a circle is \(\pi r^2\), including the circle-to-rectangle idea, radius, circumference, and area formula.

Try to answer the questions before checking the answers at the bottom of the page.

Question 1

What does the area of a circle measure?

A) Distance around the circle
B) Space inside the circle
C) Diameter of the circle
D) Radius of the circle

Question 2

What is the formula for the area of a circle?

A) \(2\pi r\)
B) \(\pi d\)
C) \(\pi r^2\)
D) \(r^2\)

Question 3

If the radius of a circle is \(4 \text{ cm}\), what is the area?

A) \(8 \pi \text{ cm}^2\)
B) \(12 \pi \text{ cm}^2\)
C) \(16 \pi \text{ cm}^2\)
D) \(32 \pi \text{ cm}^2\)

Question 4

Half of the circumference of a circle is equal to:

A) \(2 r\)
B) \(\pi r\)
C) \(r^2\)
D) \(2 \pi r\)

Question 5

What shape does the rearranged circle slices begin to look like?

A) Triangle
B) Square
C) Rectangle
D) Pentagon

Question 6

If the diameter of a circle is \(10 \text{ m}\), what is the radius?

A) \(2 \text{ m}\)
B) \(5 \text{ m}\)
C) \(10 \text{ m}\)
D) \(20 \text{ m}\)

Question 7

If the radius of a circle is:

\(r=6\text{ cm}\)

what is its area?

A) \(12\pi\text{ cm}^2\)
B) \(18\pi\text{ cm}^2\)
C) \(36\pi\text{ cm}^2\)
D) \(72\pi\text{ cm}^2\)

Question 8

A circle has radius:

\(r=2\text{ m}\)

Using:

\(\pi\approx3.14\)

what is its approximate area?

A) \(6.28\text{ m}^2\)
B) \(12.56\text{ m}^2\)
C) \(16\text{ m}^2\)
D) \(25.12\text{ m}^2\)

Question 9

When the circle is divided into slices and the slices are arranged to form a rectangle-like shape, what represents the width of this shape?

A) The diameter
B) Half of the circumference
C) The radius
D) The area of the circle

Question 10

A circle has diameter:

\(d=12\text{ cm}\)

What is its area?

A) \(12\pi\text{ cm}^2\)
B) \(24\pi\text{ cm}^2\)
C) \(36\pi\text{ cm}^2\)
D) \(144\pi\text{ cm}^2\)

Answers

B) Space inside the circle
C) \(\pi r^2\)
C) \(16 \pi \text{ cm}^2\)
B) \(\pi r\)
C) Rectangle
B) \(5 \text{ m}\)
C) \(36\pi\text{ cm}^2\)
B) \(12.56\text{ m}^2\)
C) The radius
C) \(36\pi\text{ cm}^2\)

Mulkek