Area of Circle questions with solutions are given here for students to practice and understand in detail about Area of Circle. These questions can be referred to all students irrespective of the curriculum followed to get more practice. Solving the questions on Area of circles can help the students in their tests/Exams as well as their competitive exams. Before solving the area of circle questions, revise them here
To understand the area of a circle, let us first understand the term circle.
A circle is a geometric figure which is a closed curve, whose outer curve is equidistant from the centre. To understand the formula for Area of a circle, we need to understand the definition of Radius and diameter.
Radius is the distance from the centre of the circle to the outer curve of the circle (known as the circumference)
Diameter is the distance from one end of the circle’s curve to the other end of the circle’s curve passing through the centre of the circle. In other words, it is twice the radius, passing from the centre of the circle.
More on Circles here.
The images below will help you visualise the idea of area of a circle using the area of rectangles and the area of triangles.
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- Area of circle using Area of rectangle
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- Area of circle using Area of triangle
Formula of Area of Circle
| Area of a Circle in terms of radius (r) = πr2
Area of a Circle in terms of diameter (d) = πd2/4 Value of π in rational number = 22/7 Value of π in decimals ≅ 3.14 |
The definition, formula, FAQs and more can be found at Area of circles.
Video on Area of Circle
Video Lesson on Area of Circle
Area of Circle Questions With Solutions
Let us solve a few problems in the Area of Circle.
Question 1:
Find the area of a circle, whose diameter is 63 cm.
Solution:
Given diameter is 63 cms
Area of circle in terms of diameter is πd2/4
Area = 22/7 × (63 × 63) / 4
= (22 × 9 × 63) / 4
= 12474/4
= 3118.5 sq.cm
Therefore Area of a circle with diameter as 63 cms is 3118.5 square cms
Note: Since the given problem is in diameter, we have used the formula that is related to diameter. The other way to solve this problem is to divide the diameter by 2 to get the radius and follow the regular area of the circle formula with radius.
Question 2:
Find the area of the circle whose radius is 32 units.
Solution:
Given the radius is 32 units
Area of circle = πr2
= 22/7 × 32 × 32
= (22 × 32 × 32 ) / 7
= 22528 /7
= 3218.28 sq.units
Therefore Area of a circle with radius as 32 units is 3218.28 square units
Note: Here the problem is not given in cms, meters or inches, but units. Where units can be either of the three or any other. So the solution will also have it as units instead of other measuring terminologies.
Question 3:
The area of a circle is 154 square cm. What is the radius, diameter and circumference of the circle?
Solution:
Given Area of circle is 154 sq cms
Area of circle = πr2
154 = 22/7 × r × r
154 × 7 = 22 × r × r
1078 = 22 × r × r
1078/22 = r × r
49 = r × r
49 = r2
r = √49
r = 7.
The radius of a circle with an Area of 154 is 7 cm.
Diameter: The Diameter is twice the radius
Therefore, D = 2 r
D = 2 × 7 = 14 cms
Circumference of the circle is defined as the outer cure/perimeter of the circle. The circumference of the circle is 2πr
But 2r = D
Therefore circumference is also πD
C = πD
= 22/7 × 14
= 22 × 2
= 44 cm.
The values of radius, diameter and circumference of the circle whose area is 154 sq cm is 7 cm, 14 cm and 44 cm respectively.
Question 4:
A wall is filled with circles of small, medium and large sizes. The smallest circle is of radius 2 feet, a medium circle with diameter of 8 feet and the largest circle with a radius of 8 feet. There are 4 small circles, 3 medium circles and 2 large circles. If the cost of red paint is 100 Rs/ sq feet, green paint costs 124 Rs/sq feet and golden coloured paint costs Rs 227/ sq feet. Find the total cost of the paint required if every small circle is painted red, every medium circle is painted golden and every large circle is painted green.
Solution:
The painting wall is nothing but a covering of the area on the wall which is a 2-dimensional space. Here circles need to be painted and their cost needs to be determined.
Let us first calculate the areas of all the circles.
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- Area of the small circle
The smallest circle has a radius of 2 feet. Therefore the area of the small circle will be
Area of the circle = πr2
r = 2 feet.
Area of circle = 22/7 × 2 × 2
= 88/7
= 12.57 sq feet.
Since there are 4 small circles
Total paint required for 4 circles will be a total area of 4 circles.
⇒ Area of 1 small circle = 12.57 sq. feet
⇒ Area of 4 small circles = 4 × 12.57 = 50.28
Since every small circle needs to be painted red. But there are 4 small circles that need to be painted red.
Total cost = Area of 4 small circles × cost of red paint per sq feet
= 50.28 × 100
= 5028 Rs
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- Area of medium circle
Given diameter is 8 feet
Which implies radius if 4 feet
Area of medium circle = πr2
= 22/7 x 4 x 4
= 352/7
= 50.28 sq feet
Area of 3 medium circles = 3 × Area of medium circle
= 3 × 50.28
= 150.85 sq feet
Since every medium circle needs to be painted with a golden color. But there are 3 medium circles that need to be painted.
The cost of golden colour paint is Rs 227 per foot
Total cost of colouring golden to medium circles = Area of 3 medium circles × cost of golden paint per sq feet
= 150.85 × 227
= 34242.95
= Rs 34243 (Rounding off )
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- Area of Large circle
Given radius of larger circle is 8 feet
Area of large circle = πr2
= 22/7 × 8 × 8
= 1408/7
= 201.14
Area of 2 large circles = 2 × 201.14
= 402.28 sq feet
Since every large circle needs to be painted with a green colour. But there are 2 medium circles that need to be painted.
= 2 × 201.14
= 402.28 sq feet
Total cost of colouring green to large circles = Area of 2 large circles × cost of green paint per sq feet
= 402.28 × 124
= 49882.72 Rs
= Rs 49883 (rounded off)
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- The total cost of painting all the circles with their intended colours = Cost of 4 small circles + Cost of 3 small circles + Cost of 2 large circles.
= Rs 5028 + Rs 34243 + Rs 49883
= Rs 89154
Question 5:
The area of a circle is 22176 sq cm. What is the radius of the circle?
Solution:
The area is 22176 sq cm.
But the area of circle is given by πr2
So, πr2 = 22176
22/7 × r2= 22176
r2 = (22176 × 7) / 22
r2 = 7056
r = √7056
r = 84
Radius of the circle whose Area is 22176 is 84 cms
Question 6:
The circumference of a circle is 44 cm. What is the area of the circle?
Solution:
Circumference of the circle is given as 44 cm.
2πr = 44
2 × 22/7 × r = 44
2 × 22 × r = 44 × 7
44 × r = 44 × 7
r = (44 × 7) /44
r = 7
Using the formula of the Circumference of the circle 2πr , we find the value of the radius, which is 7.
Now substituting the value of r in the formula of area of the circle.
Area of the circle = πr2
= 22/7 × 7 × 7
= 22 × 7
= 154 sq cm.
The area of the circle is 154 sq cm.
Question 7:
A customer ordered a 10-inch pizza. However, the pizza outlet delivered two 6-inch pizzas due to a system error. When the customer complained that he received less pizza, the store owner said the customer was given 2 pizzas of 6 inches which is greater than 10 inches. Did the customer really get more pizza?
Solution:
If the size of Pizza is 10 inches, then the diameter is 10 inch.
Radius = 5 inches
Area of pizza = πr2
= 3.14 × 5 × 5
= 78.5 square inches
If the size of Pizza is 6 inches, then the diameter is 6 inch
Radius = 3 inches
Area of pizza = πr2
= 3.14 × 3 × 3
= 28.26 square inches
Two 6 inch pizzas Area is
28.26 + 28. 26 = 56.52
But the area of 10 inch pizza was 78.5 square units.
Hence the customer does not get more pizza. The outlet owner’s claim is incorrect. He needs to give more than two 6-inch pizzas to prove his claim.
Question 8:
Find the area of the circle where the longest chord is 56 units.
Solution:
Given the longest chord is 56 units. We know that the diameter is the longest chord of the circle.
So given diameter = 56 units
This implies, radius = diameter /2
= 56/2 = 28 units
Area of the circle = πr2
Area of the circle = 22/7 × 28 × 28
= 22 × 4 × 28
= 88 × 28
= 2464 sq units
Question 9:
A circular park of 500m radius has a circular space of 50m radius statue at the centre. What is the area around the statue?
Solution:
Area of a circle is given by πr2
There are 2 ways to solve this problem.
- Is by calculating the area of both the circles and the difference between them gives the required solution
Area of park = 22/7 × 500 × 500 = 785714.28
Area of park = 785714 sq m (rounding off)
Area of circular space that has a statute = 22/7 × 50 × 50 = 7857.14285714
Area of circular space that has a statute = 7857 sq m (rounding off)
Area around the park = Area of park – Area of circular space that has a statute
= 785714 – 7857
= 777857 sq m
- Area around the park = Area of park – Area of circular space that has a statute
= πr12 – πr22
= π(r12 – r22) where r1 is the radius of a circular park and r2 is the radius of the circular space that has statue.
= π ( 5002 – 502)
= π (250000 -2500)
= π (247500)
= 22/7 × 247500
= 777857.14
= 777857 (rounding off)
Question 10:
A chord of 6 cm is 4 cm from the centre of the circle. Calculate the area of the circle.
Solution:
Since the chord is 4 cm from the centre, and the chord is 6 cm, we need to find the radius, which is the 3rd side of the formed triangle.
Applying Pythagoras theorem
Hypotenuse 2 = 1st Side 2 + 2nd side 2
Hypotenuse2 = 32 + 42
Hypotenuse 2= 9 + 16
Hypotenuse2 = 25
Hypotenuse2 = √25
Hypotenuse = 5 = radius of the circle
Area of the circle is πr2
Area = 22/7 × 5 × 5
= 78.57 sq cm.
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Practice Questions on Area of Circle
- A circular cricket field of diameter 140m, has 4 circular sit-outs of 5m radius which do not have grass. Calculate the area that has grass in the field.
- A chord of length 56cm is 7 cm away from the centre. Calculate the area of circle
- Calculate the unshaded area from the below image, where the radius is 7 cm and the outer side of the square is 12cm.
