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Worksheet
Explore the concepts of calculating areas related to circles, including sectors, segments, and combinations with other geometric shapes.
Areas Related to Circles - Practice Worksheet
Strengthen your foundation with key concepts and basic applications.
This worksheet covers essential long-answer questions to help you build confidence in Areas Related to Circles from Mathematics for Class X (Mathematics).
Questions
Define a sector and a segment of a circle. How do you calculate their areas?
Recall the definitions and formulas for sector and segment areas from the chapter.
How do you find the area of a quadrant of a circle? Provide a step-by-step solution for a circle with a circumference of 22 cm.
Use the circumference to find the radius first, then apply the sector area formula for 90°.
Explain how to calculate the length of an arc of a sector with a given angle and radius. Use an example with a radius of 14 cm and an angle of 30°.
The arc length is a fraction of the total circumference, based on the sector's angle.
Describe the process to find the area of a minor segment of a circle with radius 21 cm and a central angle of 120°.
Calculate the sector area first, then subtract the area of the triangle formed by the radii and chord.
What is the difference between a minor sector and a major sector? How would you calculate the area of the major sector if the minor sector's angle is 60° and the radius is 10 cm?
The major sector's angle is 360° minus the minor sector's angle. Use this in the sector area formula.
How can you determine the area between two consecutive ribs of an umbrella with 8 ribs and a radius of 45 cm?
Divide the full circle into 8 equal sectors and calculate one sector's area.
A horse is tied to a peg at the corner of a square field with a 5 m rope. Calculate the area of the field the horse can graze.
The grazing area is a sector with a 90° angle, as the field's corner limits the horse's movement.
Explain how to find the total area cleaned by a car's wiper blade that sweeps a 115° angle with a length of 25 cm.
Calculate the area for one wiper's sweep and multiply by two for the total area.
A lighthouse warns ships with a light over an 80° sector to a distance of 16.5 km. Find the area of the sea warned.
Use the sector area formula with the given angle and radius (distance).
Calculate the cost of making designs on a round table cover with six equal designs, each requiring an area calculation based on a radius of 28 cm, at a rate of ₹0.35 per cm².
Calculate one design's area as a 60° sector, then multiply by six and the cost rate.
Areas Related to Circles - Mastery Worksheet
Advance your understanding through integrative and tricky questions.
This worksheet challenges you with deeper, multi-concept long-answer questions from Areas Related to Circles to prepare for higher-weightage questions in Class X Mathematics.
Questions
A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use π = 3.14 and √3 = 1.73)
Remember to convert the angle to radians if necessary for the sine function in the area of the triangle formula.
An umbrella has 8 ribs which are equally spaced. Assuming the umbrella to be a flat circle of radius 45 cm, find the area between two consecutive ribs of the umbrella.
Calculate the central angle for one sector by dividing the total angle of the circle by the number of ribs.
A horse is tied to a peg at one corner of a square-shaped grass field of side 15 m by means of a 5 m long rope. Find the area of that part of the field in which the horse can graze.
Visualize the grazing area as a sector of a circle with a 90° angle because the field is square and the horse is tied at a corner.
Find the area of the segment AYB shown in a circle with radius 21 cm and angle AOB = 120°. (Use π = 22/7)
Use the sine of 120° which is √3/2 to calculate the area of the triangle.
A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades.
Ensure that the angle is in degrees when using the sector area formula.
To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned. (Use π = 3.14)
Convert the radius to meters or kilometers consistently in your calculations.
A round table cover has six equal designs as shown in a circle of radius 28 cm. Find the cost of making the designs at the rate of ₹0.35 per cm². (Use √3 = 1.7)
Each design is a sector of the circle with a 60° angle since the designs are equally spaced.
A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors. Find the total length of the silver wire required.
Remember that the length of one diameter is equal to the diameter of the circle.
Find the area of a quadrant of a circle whose circumference is 22 cm.
Use the value of π as 22/7 to simplify the calculations.
The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
Calculate the angle swept by the minute hand per minute first, then multiply by the number of minutes.
Areas Related to Circles - Challenge Worksheet
Push your limits with complex, exam-level long-form questions.
The final worksheet presents challenging long-answer questions that test your depth of understanding and exam-readiness for Areas Related to Circles in Class X.
Questions
A circular park of radius 20 m is surrounded by a path of width 2 m. Find the area of the path. Also, find the cost of paving the path at the rate of ₹50 per m².
Consider the path as a ring around the park. The radius of the outer circle will be the sum of the park's radius and the path's width.
An arc of a circle subtends an angle of 60° at the centre. If the length of the arc is 22 cm, find the radius of the circle.
The formula relating arc length, radius, and central angle is crucial here.
A sector of a circle with radius 14 cm has an area of 154 cm². Find the angle subtended at the centre by the sector.
The area of a sector is proportional to its central angle.
In a circle of radius 21 cm, a chord subtends an angle of 120° at the centre. Find the area of the minor segment formed by the chord.
You'll need to find the area of the triangle using trigonometry.
Two circles touch externally. The sum of their areas is 130π cm², and the distance between their centres is 14 cm. Find the radii of the two circles.
The distance between centres is the sum of the radii for externally touching circles.
A horse is tied to a corner of a square field with a rope of length 7 m. Find the area the horse can graze. What if the rope was 14 m long?
Remember, the horse is tied to a corner, so the grazable area is a quarter-circle for the shorter rope.
A circular wire of radius 42 cm is bent into the shape of a rectangle whose sides are in the ratio 6:5. Find the area of the rectangle.
The circumference of the circle equals the perimeter of the rectangle.
Find the area of the largest circle that can be inscribed in a square of side 14 cm.
Visualize the circle fitting perfectly inside the square, touching all four sides.
A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc.
The triangle formed by the two radii and the chord is equilateral if the chord equals the radius.
The minute hand of a clock is 14 cm long. Find the area swept by the minute hand in 10 minutes.
A minute hand completes 360° in 60 minutes, so in 10 minutes, it sweeps 60°.
Explore the properties, types, and theorems related to triangles, including congruence and similarity, to solve geometric problems effectively.
Coordinate Geometry explores the relationship between algebra and geometry through the use of coordinate systems to represent geometric shapes and solve problems.
Explore the basics of trigonometry, including angles, triangles, and the fundamental trigonometric ratios: sine, cosine, and tangent.
Explore real-world applications of trigonometry in measuring heights, distances, and angles in various fields such as astronomy, navigation, and architecture.
Explore the properties, theorems, and applications of circles in geometry, including tangents, chords, and angles subtended by arcs.
