Question

What is 75% of the area of a circle with a circumference of 10 units? Round the solution to the nearest square unit.

Answer 1

Answer: 6 sq. units

Step-by-step explanation:

The formula to find the circumference of a circle is given by :-

$C=2\pi r$, where r is the radius of the circle.

Given : Circumference = 10 units

Then , $10=2\pi r$

$\\\\\Rightarrow\ r=\dfrac{10}{2\pi}\approx1.59$

The area of a circle is given by :-

$A=\pi r^2=\pi(1.59)^2=7.9422603875\approx7.94\text{ sq. units}$

Now, the 75 % of the area is given by :-

$0.75\times7.94=5.955\approx6\text{ sq. units}$

Hence, 75% of the area of a circle with a circumference of 10 units = 6 sq. units

Answer 2

C=2pir
area=pir^2

so if c=10units
10=2pir
5=pir
5/pi=r

sub for area
area=pir^2
area=pi(5/pi)^2
area=pi(25/pi^2)
area=25/pi

75% or 3/4 of that is
25/pi times 3/4=75/(4pi)
use calculator
5.9683103659460750913331411264693 square units
or rounded
6 square units