Question : If the perimeter of a square is $80\;\mathrm{cm}$, then what is the diagonal (in $\mathrm{cm}$) of the square?

Option 1: $20\sqrt{2}$

Option 2: $40\sqrt{2}$

Option 3: $80\sqrt{2}$

Option 4: $20$

Question : If the length of a side of the square is equal to that of the diameter of a circle, then the ratio of the area of the square and that of the circle is:

Option 1: 14 : 11

Option 2: 7 : 11

Option 3: 11 : 14

Option 4: 11 : 7

Question : If the perimeter of a square is $44\;\mathrm{cm}$, what is the diagonal (in $\mathrm{cm}$) of the square?

Option 1: $11\sqrt{2}$

Option 2: $2\sqrt{11}$

Option 3: $11$

Option 4: $44\sqrt{2}$

Question : A sphere and another solid hemisphere have the same surface area. The ratio of their volumes is:

Option 1: $2 \sqrt{3}: 8$

Option 2: $3 \sqrt{3}: 8$

Option 3: $3 \sqrt{3}: 4$

Option 4: $\sqrt{3}: 4$

Question : The diameter of a hemisphere is equal to the diagonal of a rectangle of length 4 cm and breadth 3 cm. Find the total surface area (in cm²) of the hemisphere.

Option 1: $25 \pi$

Option 2: $\frac{75 \pi}{4}$

Option 3: $\frac{50 \pi}{4}$

Option 4: $\frac{25 \pi}{4}$