# CBSE Class 10 Maths - Area related to Circles (MCQs)

Q1: The circumference of a circle is equal to the perimeter of a square of side 11 cm. Find the area of the circle?

(a) 122 cm²

(b) 144 cm²

(c) 154 cm²

(d) 180 cm²

Q2: The radii of the two circles are 19 cm and 9 cm respectively. Find the radius of a circle that has a circumference equal to the sum of their circumferences.

(a) 28 cm

(b) 10 cm

(c) 44 cm

(d) 22 cm

Q3: If the perimeter of a protractor is 36cm, find its area?

(a) 11 cm²

(b) 14 cm²

(c) 77 cm²

(d) 308 cm²

Q4: In the figure shown, OACB is a quadrant of a circle of radius 7 cm. The perimeter of the quadrant is

(a) 11 cm

(b) 18 cm

(c) 25 cm

(d) 36 cm

Q5: Area of a circle that can be inscribed in a square of side 6cm is:

(a) 36π cm²

(b) 18π cm²

(c) 12π cm²

(d)  9π cm²

Q6: What is the area of the sector with a radius of 3.5 cm and sector angle of 60°?

(a) 12.8 cm²

(b) 6.4 cm²

(c) 44.9 cm²

(d) 269.5  cm²

Q7: The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?

(a) 2275

(b) 2650

(c) 3815

(d) 4375

Q8: The ratio of the areas of a circle and an equilateral triangle whose diameter and a side are respectively equal is

(a) $\pi : \sqrt{2}$

(b) $\pi : \sqrt{3}$

(c) $\sqrt{3} : \pi$

(d) $\sqrt{2} : \pi$

Q9: In the given figure, PSR, RTQ and PAQ are three semicircles of diameters 10 cm, 3 cm and 7 cm respectively. The perimeter of the shaded region is

[Use π = 3.14]

(a) 22.5 cm

(b) 31.4 cm

(c) 36.6 cm

(d) None of these

Q10: In a circle of radius 14 cm, an arc subtends an angle of 45c at the centre, then the area of the sector is:

(a) 71 cm²

(b) 76 cm²

(c) 77 cm²

(d) 154 cm²

1: (c) 154 cm²

a = 11cm, 2πr = 44cm ⇨ r = 7cm

⇨ Area = πr² = 154cm²

2: (a) 28 cm

2πR = 2πr₁ + 2πr₂

⇨ R = r₁ + r₂ = 9 + 19 = 28 cm

3: (c) 77 cm²

$\pi r + 2r = 36$

$\Rightarrow (\frac{22}{7})r + 2r = 36$

$\Rightarrow \frac{(22r + 14r)}{7} = 36$

$\Rightarrow 36r = 36 \times 7 \Rightarrow r = 7cm$

Area = $\frac{1}{2}\pi r^2$

Area= $\frac{1}{2}\times \frac{22}{7}\times 7^2 = 77$

4: (c) 25 cm

Permeter = πr/2 + 2r = (22×7)/(7×2) + 2×7 = 11 + 14 = 25cm

5: (d)  9π cm²

Here d = 2r = 6 ∴ r = 3cm

Area = πr² = 9π

6: (b) 6.4 cm²

$\frac{\theta}{360^{\circ}}\pi r^2$

$A = \frac{60}{360}(\frac{22}{7})(3.5)^2 = 6.42$

7: (d) 4375

8: (b) $\pi : \sqrt{3}$

9: (b) 31.4 cm

10: (c) 77 cm²