Question

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

Answer 1

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.

Answer 2

Answer:

False

Step-by-step 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;

$r = \frac{5}{\pi}$ units

Find area of circle:

$A = \pi r^2$

Substitute the value of r we have;

$A = \pi \cdot (\frac{5}{\pi})^2$

⇒$A = \pi \cdot \frac{25}{\pi^2} = \frac{25}{\pi}$

But A = 100 square units

⇒$A = \frac{25}{\pi} \neq 100$

Therefore, the given statement is FALSE