Question : A 64 cm wide path is made around a circular garden having a diameter of 10 metres. The area (in m²) of the path is closest to: (Take $\pi=\frac{22}{7}$)

Option 1: 10

Option 2: 21

Option 3: 15

Option 4: 9

Question : If the sum of the diagonals of a rhombus is $L$ and the perimeter is $4P$, find the area of the rhombus.

Option 1: $\frac{1}{4}\left(\mathrm{~L}^2-\mathrm{P}^2\right)$

Option 2: $\frac{1}{4}\left(\mathrm{~L}^2-4 \mathrm{P}^2\right)$

Option 3: $\frac{1}{2}\left(\mathrm{~L}^2-4 \mathrm{P}^2\right)$

Option 4: $\frac{1}{4}\left(\mathrm{~L}^2+3 \mathrm{P}^2\right)$

Question : A circular park whose diameter is 210 m has a 5 m wide path running around it (on the outside). What is the area (in m²) of the path?

Option 1: 1020$\pi$

Option 2: 1075$\pi$

Option 3: 1050$\pi$

Option 4: 1100$\pi$

Question : If the perimeter of circle A is equal to the perimeter of semicircle B, what is the ratio of their areas?

Option 1: $\left (x+ 2\right)^{2} : 2\pi ^{2}$

Option 2: $2\pi ^{2} : \left ( x+2 \right)^{2}$

Option 3: $\left (\pi +2 \right )^{2} : 4\pi ^{2}$

Option 4: $4\pi ^{2}:\left ( \pi +2 \right)^{2}$

Question : Three circles of equal radius '$a$' cm touch each other. The area of the shaded region is:

Option 1: $\left ( \frac{\sqrt{3}+\pi}{2} \right )a^{2}$ sq. cm

Option 2: $\left ( \frac{6\sqrt{3}-\pi }{2} \right )a^{2}$ sq. cm

Option 3: $\left ( \sqrt{3}-\pi \right )a^{2}$ sq. cm

Option 4: $\left ( \frac{2\sqrt{3}- \pi}{2} \right )a^{2}$ sq. cm