Word Problems: Circles | Mathematics for Class 5 PDF Download

Q1: Find the area of the circle whose radius is 32 units.
Ans: 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

Q2: Find the area of a circle, whose diameter is 63 cm.
Ans: 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

Q3: The circumference of a circle is 44 cm. What is the area of the circle?
Ans: 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.

Q4: The area of a circle is 154 square cm. What is the radius, diameter and circumference of the circle?
Ans: 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.

Q5: The area of a circle is 22176 sq cm. What is the radius of the circle?
Ans: 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