Question 1: Find the circumference and area of a circle of radius .

Answer:

Radius

Circumference of circle

Area of circle

Question 2: Find the circumference of a circle whose area is .

Answer:

Area

Therefore

Therefore circumference of the circle

Question 3: Find the area of a circle whose circumference is .

Answer:

Circumference

Therefore

Therefore Area

Question 4: The circumference of a circle exceeds the diameter by . Find the circumference of the circle.

Answer:

Given:

Therefore Circumference

Question 5: A horse is tied to a pole with long string. Find the area where the horse can graze.

Answer:

Area that the horse can graze

Question 6: A steel wire when bent in the form of a square encloses an area of . If the same wire is bent in the form of a circle, find the area of the circle.

Answer:

Area of square

Let the side of the square

Therefore Perimeter

Let be the radius of the circle

Therefore

Therefore Area of circle

Question 7: The diameters of the front and rear wheels of a tractor are and respectively. Find the number of revolutions that rear wheel will make to cover the distance which the front wheel covers in revolutions.

Answer:

Diameter of front wheel

Diameter of rear wheel

Distance covered by front wheel

Let no of revolution that the rear wheel

Therefore

Question 8: A copper wire when bent in the form of a square encloses an area of . lf the same wire is bent into the form of a circle, find the area of the circle.

Answer:

Area of square

Let the side of the square

Therefore Perimeter

Let be the radius of the circle

Therefore

Therefore Area of circle

Question 9: The circumference of two circles are in the ratio . Find the ratio of their areas.

Answer:

Let the radius of first circle

Let the radius of second circle

Therefore

Therefore Ratios of their areas

Question 10: The side of a square is . Find the area of circumscribed and inscribed circles.

Answer:

When square is inscribed in the circle

Therefore diameter

Therefore radius of circle

Therefore are of circle

When the circle is inscribed in the square

Diameter

Therefore radius

Therefore Area of circle

Question 11: The sum of the radii of two circles is and the difference of their circumferences is . Find the diameters of the circles.

Answer:

Let the two radii be and

Therefore … … … … … i)

… … … … … ii)

From i) and ii)

Therefore

Therefore

Diameter of circles are and

Question 12: Find the area of the circle in which a square of area is inscribed. Take

Answer:

Area of square

Side of square

Diameter of circle

Radius of the circle

Hence Area of circle

Question 13: A field is in the form of a circle. A fence is to be erected around the field. The cost of fencing would be at the rate of per meter. Then, the field is to be thoroughly ploughed at the cost of . What is the amount required to plough the field? Take

Answer:

Cost of fencing

Circumference of the field

Therefore

Area of the field

Therefore cost of ploughing

Question 14: If square is inscribed in a circle, find the ratio of the areas of the circle and the square.

Answer:

Let the side of the square

Therefore diameter of circle

Therefore radius of the circle

Therefore ratios of their areas

Hence the ratios of their area is

Question 15: A park is in the form of a rectangle . At the center of the park there is a circular lawn. The area of park excluding lawn is . Find the radius of the circular lawn. Take

Answer:

Let the radius of the circle

Area of the park

Are of circle

Therefore

Therefore

Question 16: The radii of two circles are and respectively. Find the radius of the circle having its area equal to the sum of the areas of the two circles.

Answer:

Let the radius of the circle

Therefore

Question 17: The radii of two circles are and respectively. Find the radius and area of the circle which has its circumference equal to the sum of the circumferences of the two circles.

Answer:

Let the radius of the circle

Therefore

Therefore Area

Circumference

Question 18: A car travels 1-kilometer distance in which each wheel makes complete revolutions. Find the radius of its wheels.

Answer:

Let the radius of the wheel

Therefore

Question 19: The area enclosed between the concentric circles is . If the radius of the outer circle is , find the radius of the inner circle.

Answer:

Let the radius of the inner circle

Therefore

Therefore

Question 20: The wheel of a car is making revolutions per second. If the diameter of the wheel is , find its speed in . Give your answer, correct to nearest km.

Answer:

No. of revolutions per second

Radius of the wheel

Therefore circumference of the wheel

Hence the distance covered in 1 second

Hence distance covered in one hour

Question 21: A sheet is long and wide. Circular pieces of in diameter are cut from it to prepare discs. Calculate the number of discs that can be prepared.

Answer:

Number of disks by length

No of disks by breadth

Therefore total number of disks that can be cut

Question 22: A copper wire when bent in the form of an equilateral triangle has area . If the same wire is bent into the form of a circle, find the area enclosed.

Answer:

Let the side of the equilateral triangle

Therefore

Therefore

Therefore perimeter

Let the radius of the circle

Therefore

Area of circle