Question : The area of the sector of a circle of radius 12 cm is $32 \pi \;\mathrm{cm}^2$. Find the length of the corresponding arc of the sector.

Option 1: $\frac{16}{3} \pi$ cm

Option 2: $\frac{13}{3} \pi$ cm

Option 3: $\frac{10}{3} \pi$ cm

Option 4: $\frac{8}{3} \pi$ cm

Question : The area of a rhombus is 256 square cm, and one of its diagonals is twice the other in length. The length of its larger diagonal is:

Option 1: 32 cm

Option 2: 16 cm

Option 3: 48 cm

Option 4: 24 cm

Question : The radius of a circle is 5 cm. The length of chord AB in this circle is 6 cm. What is the distance of this chord from the centre of the circle?

Option 1: 4 cm

Option 2: 5 cm

Option 3: 6 cm

Option 4: 8 cm

Question : A chord of length 40 cm is drawn in a circle having a diameter of 50 cm. What is the
a minimum distance of another parallel chord of length 30 cm in the same circle from a 40 cm long chord?

Option 1: 10 cm

Option 2: 15 cm

Option 3: 5 cm

Option 4: 20 cm

Question : The length of the chord of a circle is 24 cm, and the perpendicular distance between the centre and the chord is 5 cm. The radius of the circle is:

Option 1: 10 cm

Option 2: 13 cm

Option 3: 12 cm

Option 4: 24 cm