Question : A is the centre of a circle whose radius is 8 units, and B is the centre of a circle whose diameter is 8 units. If these two circles touch externally, then the area of the circle with diameter AB is:

Option 1: $36\pi$ sq. units

Option 2: $64\pi$ sq. units

Option 3: $144\pi$ sq. units

Option 4: $256\pi$ sq. units

Question : ABCD is a square inscribed in a circle of radius $r$. Then the total area (in square units) of the portions of the circle lying outside the square is:

Option 1: $\pi (r^{2}-4)$

Option 2: $2\pi (r ^{2}-1)$

Option 3: $\pi^{2} r(r-7)$

Option 4: $r^{2}(\pi -2)$

Question : The area of triangle formed by the straight line $3x + 2y = 6$ and the co-ordinate axes is:

Option 1: 3 square units

Option 2: 6 square units

Option 3: 4 square units

Option 4: 8 square units

Question : A circle and a square have the same area. The ratio of the side of the square to the radius of the circle will be:

Option 1: $\sqrt\pi:1$

Option 2: $1:\sqrt\pi$

Option 3: $(\pi)^2:1$

Option 4: $1:\sqrt2\pi$

Question : A metallic solid spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 2 cm and 1.5 cm. What is the surface area (in cm²) of the third ball?

Option 1: $50 \pi$

Option 2: $\frac{25}{4} \pi$

Option 3: $25 \pi$

Option 4: $\frac{25}{2} \pi$