This topic focuses on determining the full area of a circle from the given area of a sector. Skills practiced include calculating the area of circular sectors, understanding fractions of whole circles, and applying the value of pi (π) in arithmetical operations, all within the context of basic geometry involving circles. Each problem provides a fraction of a circle's area, and students must calculate the area of the whole circle based on the given sector's area. This offers valuable practice in applying geometric and proportional reasoning skills.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

more
View

Area of a Part Circle - Part Area and Fraction to Full Area (Pi Value) Worksheet

Mobius Math Academy logo
Area of a Part Circle - Part Area and Fraction to Full Area (Pi Value)
1
An svg image showing a math problem
The area of the green shaded 1/4 sector is 1π. What is the area of the full circle?
a A LaTex expression showing 3Pi
b A LaTex expression showing 7 over 4 Pi
c A LaTex expression showing 4Pi
d A LaTex expression showing 2Pi
e A LaTex expression showing 13 over 4 Pi
2
An svg image showing a math problem
The area of the green shaded 3/5 sector is 108/5π. What is the area of the full circle?
a A LaTex expression showing 27 over 5 Pi
b A LaTex expression showing 6 over 5 Pi
c A LaTex expression showing 36Pi
d A LaTex expression showing 12 over 5 Pi
3
An svg image showing a math problem
The area of the green shaded 1/3 sector is 12π. What is the area of the full circle?
a A LaTex expression showing 36Pi
b A LaTex expression showing 3Pi
c A LaTex expression showing 4Pi
d A LaTex expression showing 16Pi
e A LaTex expression showing 6Pi
4
An svg image showing a math problem
The area of the green shaded 4/5 sector is 144/5π. What is the area of the full circle?
a A LaTex expression showing 36Pi
b A LaTex expression showing 6Pi
c A LaTex expression showing 42 over 5 Pi
d A LaTex expression showing 51 over 5 Pi
5
An svg image showing a math problem
The area of the green shaded 1/4 sector is 25/4π. What is the area of the full circle?
a A LaTex expression showing 25Pi
b A LaTex expression showing 27 over 4 Pi
c A LaTex expression showing 7 over 4 Pi
d A LaTex expression showing 41 over 4 Pi
e A LaTex expression showing 13 over 4 Pi
6
An svg image showing a math problem
The area of the green shaded 1/3 sector is 3π. What is the area of the full circle?
a A LaTex expression showing 5 over 3 Pi
b A LaTex expression showing 9Pi
c A LaTex expression showing 10 over 3 Pi
d A LaTex expression showing 1 over 3 Pi
7
An svg image showing a math problem
The area of the green shaded 2/5 sector is 18/5π. What is the area of the full circle?
a A LaTex expression showing 3 over 5 Pi
b A LaTex expression showing 9Pi
c A LaTex expression showing 18 over 5 Pi
d A LaTex expression showing 1 over 5 Pi
e A LaTex expression showing 11 over 5 Pi
8
An svg image showing a math problem
The area of the green shaded 3/5 sector is 27/5π. What is the area of the full circle?
a A LaTex expression showing 3 over 5 Pi
b A LaTex expression showing 9Pi
c A LaTex expression showing 16 over 5 Pi
d A LaTex expression showing 7 over 5 Pi
e A LaTex expression showing 1Pi