Areas Related to Circles Questions with answers are provided here. Class 10 students can practise the questions based on areas related to circles to prepare for the exams. These areas related to circles problems are prepared by our subject experts as per the latest exam pattern. All the materials here are formulated according to the NCERT curriculum and latest CBSE syllabus (2022-2023). Learn more: Areas Related to Circles Class 10 Notes.
Formulas of Areas Related to Circles:
- Area of circle = πr2
- Circumference of circle = 2Ï€r
- Length of an arc of a sector = L= (θ/360°)×2πr
- Area of a sector of circle = (θ/360°)×πr2
Areas Related to Circles Questions and Solutions
Q.1: If the radius of a circle is 4.2 cm, find its area.
Solution: Given,
Radius of circle = 4.2 cm
By the formula, we have;
Area of circle = πr2
A = π(4.2)2
A = 55.44 cm2
Q.2: If the area of a circle is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm, calculate the diameter of the larger circle.
Solution: Given,
Diameter of a circle, d1 = 10 cm
Radius, r1 = 10/2 = 5cm
diameter of another circle, d2 = 24 cm
Radius, r2 = 24/2 = 12cm
According to the question;
Area of a circle = area of circle 1 + area of a circle 2
So,
πR2 = πr12 + πr22
πR2 = π(r12 + πr22)
R2 = 52 + 122 = 25 + 144
R2 = 169 = 13 cm
Therefore, required diameter = 2(13) = 26 cm
Q.3: The circumference of a circular field is 528 m, find the radius of the field.
Solution: Given,
Circumference = 528 m
Hence,
2Ï€R=528 [by circumference formula]
R = 528/2Ï€
R = (528 x 7)/(2 x 22)
R = 84 cm
Q.4: The area of a circular ring formed by two concentric circles whose radii are 5.7 cm and 4.3 cm, respectively.
Solution: Let the radii of inner and outer circles be r1 and r2, respectively.
Area of circular ring = area of outer circle – area of inner circle
= Ï€ r22 – Ï€ r12
= Ï€ (r22 – Ï€ r12)
= Ï€ (r2 – r1) (r2 + r1)
= =π(5.7−4.3)(5.7+4.3)
= π×1.4×10 sq. cm
=3.1416×14sq.cm.
=43.98 sq. cm
Q.5: What is the area of the circle that can be inscribed in a square of side 6 cm?
Solution: Given,
Square of side = 6 cm
Diameter of circle inscribed in the square = side of square = 6cm
Radius = 6/2 = 3 cm
Hence,
Area of the circle inscribed = πr2
= π(3)2
= 9Ï€ cm2
Q.6: The circumference of a circle increases from 4Ï€ to 8Ï€. Find the ratio of areas.
Solution: Let us say,
Circumference of first circle, C1 = 4Ï€
2Ï€r1 = 4Ï€
r1 = 2
Circumference of new circle, C2 = 8Ï€
2Ï€r2 = 8Ï€
r2 = 4
Area of old circle, A1 = πr12
Area of new circle, A2 = πr22
A1/A2 = (Ï€r12/Ï€r22)
= (r1/r2)2
= (2/4)2
= (½)2
= ¼
Therefore, the ratio of the areas of circles is 1:4.
Q.7: What is the area of the sector of a circle of radius 6 cm whose central angle is 30°?
Solution: Given,
Radius of circle = 6 cm
Central angle, θ=30°
Area of sector = θ/360 (πr2)
= 30/360 (Ï€62)
= 9.42 cm2
Q.8: The radius of a circle is 17.5 cm. What is the area of the sector of the circle enclosed by two radii and an arc 44 cm in length?
Solution: Given,
Radius of a circle = 17.5 cm
Length of arc of circle = 44 cm
Area of sector = ½ × Arc Length × Radius
= ½ × 44 × 17.5
= 385 cm2
Q.9: A park is of the shape of a circle of diameter 7 m. It is surrounded by a path with a width of 0.7 m. If its cost is Rs.110 per sq. m., what is the expenditure of cementing the path?
Solution: Given,
Diameter of park = 7 m
Radius of park, r = 7/2 = 3.5 m
Width of park = 0.7 m
Radius of park along with path, R = 3.5 + 0.7 = 4.2 m
Cost per square meter = Rs.110
Area of path = Area of outer circle – area of inner circle
= Ï€R2 – Ï€r2
= Ï€(R2 – r2)
= 22/7 (4.22 – 3.52)
= 22/7 (17.64 – 12.25)
= 16.94 m2
Cost of expenditure of cementing the path = Rs. 110x 16.94 = Rs.1863.40
Q.10: The circumference of a given circular park is 55 m. It is surrounded by a path of uniform width 3.5 m. Find the area of the path.
Solution: Let r be the radius of the circular park.
2Ï€r=55
r = 55/2Ï€ = 8.75 m
Area of park = π × (8.75)2 = 240.625 m2
Radius of the circular park with path, R = 8.75 + 3.5 = 12.25 m
Area of circular region is A = π × (12.25)2 = 471.625 m2
Area of the path surrounding the circular park = 471.625−240.625=231m2
Video Lessons on Circles
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Area of a Circle
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