Mensuration 3D

Question 1

Given: A water tank is being used to supply drinking water in a city due to a shortage of water. If the dimensions of the tank are 7m in length, 11m in breadth, and 3.5m in height. Find how many liters of water can be filled in the tank?

• 128,700 lt.

• 225,535 lt.

• 269,500 lt.

• 324,600 lt.

Question 2

If Jimmy rolls a sheet of paper initially square-shaped along its length to make it a cylinder. Find what will be the ratio of the base radius of the cylinder to the side of the square?

• 1/2π

• 7/2π

• 9/π

• 11/2π

Question 3

Given: A 5 cm cube which is cut into as many smaller cubes of 1 cm as possible. Find what will be the ratio of the surface area of the original cube to that of the sum of the surface areas of all the smaller cubes formed after cuttting? 

• 5:4

• 5:1

• 6:7

• 1:5

Question 4

Given: A cubical wooden structure with sides of 5 cm is painted on all its faces. If the cubical structure is sliced into 1 cm cubes, find how many 1 cm cubes will have exactly one of their faces painted?

• 33

• 54

• 76

• 140

Question 5

A drum is full of water. Diameter of the drum is 35cm. The level of water will be dropped by how much, if 11 litres of water is taken out:

• 40/7
• 80/7
• 70/9
• 13/8

Question 6

Given: A hemispherical bowl is filled to the brim with water. The content of the bowl i.e. water is transferred into a cylindrical vessel whose radius is 50% more than its height. If the diameter is the same for both the bowl and the cylinder, find the volume of water in the cylindrical vessel.

• 33.33%

• 66.66%

• 50%

• 100%

Question 7

A metallic hemisphere is melted and recast in the shape of a cone with the same base radius (R) as that of the hemisphere. If H is the height of the cone, then:

• H = 2R
• H = 3R
• H = 2/3R
• H = 3/2R

Question 8

A hemisphere and a cone have equal bases. If their heights are also equal, then the ratio of their curved surfaces will be:

• 1:2
• 2:1
• 1:2^0.5
• 2^0.5:1

Question 9

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. The height of the cone is:

• 12 cm
• 14 cm
• 15 cm
• 18 cm

Question 10

A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm. The height of the cone is:

• 2 cm
• 3 cm
• 4 cm
• 6 cm