Question : Some ice pieces, spherical in shape, of diameter 6 cm are dropped in a cylindrical container containing some juice and are fully submerged. If the diameter of the container is 18 cm and the level of juice rises by 40 cm, then how many ice pieces are dropped in the container?

Option 1: 95

Option 2: 85

Option 3: 80

Option 4: 90

Question : Some medicine in liquid form is prepared in a hemispherical container of diameter 36 cm. When the container is full of medicine, the medicine is transferred to small cylindrical bottles of diameter 6 cm and height 6 cm. How many bottles are required to empty the container?

Option 1: 76

Option 2: 72

Option 3: 70

Option 4: 75

Question : A hemispherical bowl of internal diameter 18 cm contains water. This water is to be filled in cylindrical bottles of diameter 6 cm and height 3 cm. The number of bottles required to empty the bowl is:

Option 1: 3

Option 2: 9

Option 3: 6

Option 4: 18

Question : The length of the common chord of two intersecting circles is 24 cm. If the diameter of the circles are 30 cm and 26 cm, then the distance between the centres (in cm) is:

Option 1: 16 cm

Option 2: 14 cm

Option 3: 18 cm

Option 4: 12 cm

Question : A tap is dripping at a constant rate into a container. The level L cm of the water in the container is given by the equation L = $2-2^t$, where t is the time taken in hours. What is the level of water in the container at the start?

Option 1: 0 cm

Option 2: 1 cm

Option 3: 2 cm

Option 4: 4 cm

Question : A hollow cylindrical tube made of plastic is 3 cm thick. If the external diameter is 20 cm and the length of the tube is 49 cm, find the volume of the plastic.

Option 1: 7238 cm³

Option 2: 7644 cm³

Option 3: 7546 cm³

Option 4: 7854 cm³