Strategies and Tricks to Solve Circle Question

What is the radius of a circle if its perimeter is numerically equal to thrice its area?

A. 2

B. 3

C. 2/3

D. 4

Answer : Option C
2πr = 3πr²
⇒ r = 2/3
The area of the sector of a circle, whose radius is 12 metres when the angle at the centre is 60, is

A. 13.2 m²

B. 75.42 m²

C. 13.4 m²

D. None of these

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Answer : Option A
Area of the sector r = πr²θ/360. θ = 60°, and radius = 12m So area = (22/7) × (12×12×60 / 360) ⇒ = 75.42m²
Find the radius of the circle if area of sector is 924cm2 and angle at the center is 60.

A. 42

B. 21

C. 22

D. 46

Answer : Option A
A= πr² × 60/360 = 924
&⇒ r =42
The difference between the circumference and area of a circle is 110 metres. Find its circumference.

A. 44m

B. 84m

C. 30m

D. 7m

Answer : Option A
πr² - 2Πr = 110
⇒ r= 7
Circumference = 2×22/7×7 = 44
When the radius of a circle is decreased by 100%, the area of the circle:

A. decreases by 50%

B. decreases by 100%

C. increases by 100%

D. decreases by 200%

Answer : Option B
Since the radius of circle is reduced by 100%, the radius becomes 0.
Therefore, area also decreases to 0.
So, the area of the circle decreases by 100%.

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Find circumference of a circle if area of the circle is 154 cm².

A. 18

B. 22

C. 44

D. 66

Answer : Option A
22/7 ×r² = 154 r = 7 Circumference = 2×22/7×7 =44 cm
The difference between the circumference and the diameter of the circle is 60 cm. The area of the circle is:

A. 425 cm2

B. 616

C. 154cm²

D. 308 cm²

Answer : Option B
πD-D=60
D=60/(π-1)=60/(15/7)=28
Now area = π/4 × D² = 616cm²
The circle is 21 cm and m (arc RYS) = 60°. Find the area of the sector.

A. 38.5 cm²

B. 231 cm²

C. 25.66 cm²

D. 6.42 cm²

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Answer : Option B
Area of circle = π × 21×21×60/360 = 231cm²
A regular hexagon is inscribed in a circle of radius 10 cm. Find the area of the shaded portion. (× ≈ 3.14 ; √3 ≈ 1.73).

A. 271 cm²

B. 54.5 cm²

C. 290 cm²

D. 75 cm²

Answer : Option B
Area of circle = π × 10² = 3.14 × 100 = 314 cm².
Area of regular hexagon = 6 × √3 / 4 × 10 × 10 = 259.5cm².
Area of shaded region = area of circle – area of hexagon = 314 – 259.5 = 54.5cm². .
The radius of a circle is decreased by 40%. What will be the percentage decrease in its surface area?

A. 64%

B. 36%

C. 20%

D. 10%

Answer : Option A
New area = 0.6 × 0.6 of the initial area= 0.36 of the initial area.
So, 64% decrease.

Circles Practice Questions: Level 01