 Important for :
1
The area of a sector of a circle of radius 36 cm is 72π cm2. The length of the corresponding arc of the sector is
» Explain it
D
Given that, radius (r) = 36 cm

And, Area of sector = 72π cm2

 ⇒ πr2Θ = 72π 360°

 ∴  Θ = 72π × 360° πr2

 = 72 × 360° = 20° 36 × 36
 Now, length of arc = πrΘ 180°
 = π × 36 × 20° = 4π cm 180°
Hence, optiion D is correct.

2
A square is inscribed in a circle of diameter 2a and another square is circumscribing circle. The difference between the areas of outer and inner squares is
» Explain it
B Given that, Diameter = 2a

For inscribed square,

Diameter of circle = Diagonal of inner square

For circumscribed square,

Diameter of circle = Side of outer square

∴  Area of inner square =

 1 (diagonal)2 = 1 × (2a)2 = 2a2 2 2

And, Area of outer square = (side)2 = (2a)2 = 4a2

Now, Required difference = 4a2 – 2a2 = 2a2

Hence, option B is correct.

3
ABC is a triangle right angled at A. AB = 6 cm and AC = 8 cm. Semi-circles drawn (outside the triangle) on AB, AC and BC as diameters which enclose areas x, y and z square units, respectively. What is x + y – z equal to ?
» Explain it
C Given that, AB = 6 cm and AC = 8 cm

In ΔABC, by Pythagoras theorem,

BC = AB2 + AC2 = 62 + 82 = 100 = 10 cm

Now, Area of that semi-circle which diameter is AB =

 π(3)2 2
 ∴  x = 9π cm2 2
Similarly, Area of that semi-circle which diameter is AC =

 π(4)2 2
 ∴  y = 16π cm2 2
Similarly, Area of that semi-circle which diameter is BC =

 π(5)2 2
 ∴  z = 25π cm2 2

Now, x + y – z =

 ( 9π + 16π ) – 25π = 0 2 2 2

Hence, option C is correct.

4
Consider an equiateral triangle of a side of unit length. A new equilateral triangle is formed by joining the mid-points of one, then a third equilateral triangle is formed by joining the mid-points of second. The process is continued. The perimeter of all triangles, thus formed is
» Explain it
C Perimeter of all triangles

= (3 × 1) + (3 × 0.5) + (3 × 0.25) + (3 × 0.125)

= 3 + 1.5 + 0.75 + 0.375 = 5.625 ≈ 6 units

Hence, option C is correct.

5
If AB and CD are two diameters of a circle of radius r and they are mutually perpendicular, then what is the ratio of the area of the circle to the area of the ΔACD ?
» Explain it
B Required ratio

= Area of circle : Area of ΔACD

 = πr2 : 1 × 2r × r   =   π 2

Hence, option B is correct.