Question : The radius of a metallic spherical ball is 3 cm. If the metallic ball is melted and recast into $x$ number of hemispheres of radius equal to half the radius of the metallic spherical ball, then find the value of $x$.

Option 1: 15

Option 2: 14

Option 3: 16

Option 4: 13

Question : A spherical lead ball of radius 10 cm is melted and small lead balls of radius 5 mm are made. The total number of possible small lead balls is (Take $\pi =\frac{22}{7}$)

Option 1: 8000

Option 2: 400

Option 3: 800

Option 4: 125

Question : A sector is formed by opening out a cone with a base radius of 8 cm and height of 6 cm. Then the radius of the sector is (in cm):

Option 1: 4

Option 2: 8

Option 3: 10

Option 4: 6

Question : A cylinder of height 8 cm and radius 6 cm is melted and converted into three cones of the same radius and height of the cylinder. Determine the total curved surface area of cones.

Option 1: $180 \pi\operatorname{cm^2}$

Option 2: $60 \pi\operatorname{cm^2}$

Option 3: $144 \pi\operatorname{cm^2}$

Option 4: $120 \pi\operatorname{cm^2}$

Question : A cylinder has some water in it at a height of 16 cm. If a sphere of radius 9 cm is put into it, then find the rise in the height of the water if the radius of the cylinder is 12 cm.

Option 1: 8 cm

Option 2: 6 cm

Option 3: 8.75 cm

Option 4: 6.75 cm