Question

A circle with circumference of 10 has area of 100.
True or False

Answer 1

False

Explanation:

Circumference(C) and Area(A) of the circle is given by:

`C = 2 \pi r`

`A = \pi r^2`

where, r is the radius of the circle.

As per the statement:

A circle with circumference of 10 has area of 100.

Circumference = 10 units

then;

`2 \pi r = 10`

Divide both sides by
`2 \pi` we have;

`r = (5)/(\pi)` units

Find area of circle:

`A = \pi r^2`

Substitute the value of r we have;

`A = \pi \cdot ((5)/(\pi))^2`

⇒
`A = \pi \cdot (25)/(\pi^2) = (25)/(\pi)`

But A = 100 square units

⇒
`A = (25)/(\pi) \\eq 100`

Therefore, the given statement is FALSE

Answer 2

Circumference of a circle:
C = 2 r π
10 = 2 r π
r = 10 / 2π = 5 / π
Area of a circle:
A = r² π = ( 5 / π )² * π = 25 / π² * π = 25 / π ≠ 100
Answer: False.