Area Related to Circles Important Questions

Areas related to Circle explain the different areas of a circle. Some of the important area related to circles formula include:

• Circumference of a circle = 2πr
• Area of a circle = πr²
• Arc’s length of the sector with degree measure and radius r = (θ/360)2πr
• Area of sector with degree measure θ and radius r = (θ/360)πr²
• Area of a segment of a circle = Area of the corresponding sector - Area of Corresponding Triangle

Area Related To Circle Class 10 Formulas

A circle's area is the area that it takes up in a two-dimensional plane. It can be simply calculated using the formula A = πr², where r is the circle's radius. The square unit, such as m², cm², etc., is the unit of area. Thus,

Area of Circle = πr² or πd²/4, square units

where, π = 22/7 or 3.14

Read more: Standard Equation of a Circle

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Very Short Answer Questions. [1 Mark Questions]

Ques. What does the expression "area of the circle" mean?

Ans. In area related to circle class 10, The region that a circle occupies in two dimensions is known as its area of circle.

Ques. If the radius is 6 cm, calculate the area of the circle in terms of π.

Ans. The area of circle is represented by the formula πr²

Here, A = π(6)² 

Thus, A = 36π.

So, if a circle has a radius of 6 cm, its area is 36π cm².

Ques. The area of a circle is 300 cm², thus calculate its radius.

Ans. Area of circle = πr²

300 = πr²

300 = 22 / 7 × r²

r² = 95

r = 9.7 cm

Ques. State true or false. Perimeter of circle is known as the circumference of the circle.

Ans. True. The perimeter of a two-dimensional shape is the path that encircles its outline. The circumference of a circle is another name for its perimeter.

Ques. What is formula for the area of semi-circle.

Ans. Area of semi-circle = πr² / 2

Because semi-circle is the half of full circle.

Ques. When the diameter of a circle is known, find the area of the circle.

Ans. Twice the radius and diameter of the circle are equal.

The formula for area of circle, considering its diameter, is π /4 diameter².

Read More:

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Short Answers Questions [2 Marks Questions]

Ques. What is the size of a circle with a 40 cm circumference?

Ans. The Circumference of circle = 2πr

Given in the question,

2πr = 40

r = 40 / 2π = 20 / π

Now, Area of Circle = πr²

= π × 20 / π × 20 / π

=127 cm²

Ques. Explain the steps to find the area of circle.

Ans. Below are some of the steps needed to determine the circle's area:

• Step 1. Mark the circle's radius as the first step.
• Step 2: Substitute the radius's value and π as constant, which has a value of 3.14, in the formula A = πr² (approx)
• Step 3: Determine the required area of the circle using the response from step 2. It has a square unit of measurement.

Ques. How do you determine the area of circle using different formulas?

Ans. The following mentioned formulas are used to determine the area of a circle:

• Area = πr²  , here 'r' stands for the radius.
• Area = (π / 4) × d², here 'd' stands for the diameter.
• Area = C² / 4π, here 'C' stands for the circumference.

Ques. If the circle has an 8 unit of circumference. Determine its area.

Ans. We are aware that the circle's circumference equals 8 units (given in the question)

By using the above mentioned formulas,

alternative C = 8

Since we are aware, value = 3.14

8 × 8 / (4 × 3.14) = 28.26

The surface area of circle is 5.09 square units as a result.

Ques. The form of a large rope is round. It has a 5 unit radius. What's the area of that rope?

Ans. Since a large rope has a circular shape and resembles a circle, we may apply formulas for circles to determine its area.

The radius is known to be r = 5 units.

So, using the above mentioned formulas:

Area of circle = πr²

Since we are aware, value of π = 3.14

3.14 × 5 × 5 = 78.50

Consequently, the circle's surface area is 78.50 square units.

Ques. Determine the area of plate whose radius is 10 cm.

Ans. Radius of a plate given in the question is 10 cm.

So we know that,

Area of circle= πr²

= 22 / 7 × 10 × 10

= 314 cm²

Thus, area of a plate is 314 sq. cm 

Ques. Explain the relationship between the area of circle and the area of square.

Ans. When the circle's diameter and the square's side length are equal, the area of a circle is thought to be 80% of the area of a square.

Thus, we have to insert a circular object into a square shape with the same side length and diameter. The area of a circle will be roughly 80 square units if the area of a square is 100 square units. This is how both area of a circle and the area of a square are interrelated.

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Long Answer Questions [3 Marks Questions]

Ques. A circle has a 12 cm radius, determine its circumference and area.

Ans. According to the question,

Radius of a circle = 12 cm

Circumference of a circle = 2πr

Circumference of a circle = 2 × 22 / 7 × 12

Circumference of Circle = 75.4 cm

Now, the area of circle = πr²

Area of circle = 22 / 7 × 12 × 12

Area of circle = 452.16 cm²

Ques. Determine the area of a sector with a 60° angle. The circle's radius is 6 cm, as given.

Ans. Given in the question that,

The sector's angle is equal to 60°.

By applying the formula,

Sector area is equal to (θ / 360°) r².

= (60° / 360°) × π r² cm²

Alternately, the sector's area is:

= 6 × 22 / 7 cm² 

= 132 / 7 cm².

Read Also: Sector of a Circle: Derivations, Perimeter and Area

Ques. A quadrilateral ABCD has been provided by a girl to circumscribe a circle as shown in the figure. Thus, prove that AB + CD = AD + BC.

Ans. From the above figure, we can see:

(i) DR = DS

(ii) BP = BQ

(iii) AP = AS

(iv) CR = CQ

Because these are tangents on the circle from the given points D, B, A, and C respectively.

Thus, by adding the LHS and RHS of the above equations, we will get:

DR + BP + AP+ CR = DS + BQ + AS + CQ

After rearrangement:

(DR + CR) + (BP + AP) = (CQ + BQ) + (DS + AS)

After simplification, we can get,

AD + BC = CD + AB

Also Read:

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Very long Answer Questions [5 Marks Questions]

Ques. Find the area of the circle if the longest chord of the circle is 14 cm.

Ans. Considering that a circle's longest chord is 14 cm in length.

We know that a circle's diameter is its longest chord.

Therefore, d = 14 cm.

R = d / 2 = 14 / 2 = 7 cm, thus.

The following is the formula for calculating the area of a circle:

A = πr².

When we change the formula to read r = 6 cm, we get

A = (22/7) × 7 × 7 cm²

A = 22 × 7 cm²

A = 152 cm²

As a result, the circle's area is 113.14 cm².

Ques. At a price of Rs. 24 per metre, fencing a circular field will cost Rs. 5280. The field must be tilled at a cost of Rs. 0.50 per square metre. Calculate the cost of field preparation.

Ans. Total cost / Rate = 5280 / 24 = 220 metres for the fence's length.

Therefore, the field's circumference is 220 metres.

If the field's radius is r metres, then 2πr = 220.

2 × (22/7) × r = 220

r = (220 × 7) / (2 × 22)

r = 35

Consequently, the field's radius is 35 metres.

Field's area is equal to πr².

= (22/7) × 35 × 35

= 22 × 5 × 35 m²

= 3850 sq. m.

1 square metre of the field will cost Rs. 0.50 to plough.

Therefore, the overall expense of preparing the field is 3850 × 0.50 = 1925 Rs.

Ques. A automobile has wheels that are each 80 cm in diameter. How many full rotations do each tyre make in ten minutes when the vehicle is moving at 66 km/h?

Ans. Since D = 80 cm, the radius of a car's wheel is 80 / 2, or 40 cm.

Thus, the wheels' circumference is 2πr x 80 cm.

Now, the distance travelled in one revolution equals the wheel's diameter, which is 80 centimetres.

Given that a car can go 66 kilometres in an hour.

When we convert km to cm, we have,

(66 × 10⁵) cm is the distance travelled by the car in one hour.

The rate of travel in 10 minutes is (66 x 10⁵ x 10) / 60, or 1100000 cm/s.

Car travel distance is equal to 11 × 10⁵ cm.

Now, the number of wheel spins = 11 × 10⁵ / 80π = 4375

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